OK, I have a laptop and need a new power supply (the cord going from the wall to the 'puter). The one that came with it is 18.5V, 3.5A. I went looking online and found a place selling what they said was the power cord and converter for this model laptop…except it was 19V, 5A. that’s not the same, will using it harm my laptop? If not, could I use another converter I have lying around from a previous laptop that outputs 16.5V and 4.5A? I always assumed that the output had to be exactly the same, does it?
You generally want to try and match the adapter specs as closely as possible. Assuming the amps meet at least the baseline for the prior adapter and the polarity and adapter plug are correct a .5 volt difference is probably withing the range of toleration for the electronics, but the charging circuit would be happiest with the exact correct spec.
I’ve generally found I can get correctly spec’d notebook power adapters on eBay for relatively little money. What is your notebook brand and model #?
The difference between 19 V and 18.5 V is small enough I wouldn’t worry; in general, you should try to match the voltage as closely as possible. Laptops (and most other relatively sophisticated electronics) have input conditioning circuitry which regulates and smooths the incoming power to match the requirements of the device. The current capacity of the power supply must be at least as large as the device requires, but there is no practical limit to high high it can be–the laptop will simply draw what it needs. You do want to be sure that this power supply is designed to power the laptop in question, since there are other factors to consider, such as plug form factor (what type, how many pins, etc.) and polarity. If you’re sure it is, given the characteristics you’ve included here, I’d say go ahead and use it. Be warned, however, that you generally get what you pay for with inexpensive third-party accessories.
It’s an LG LS50. We would like to buy directly from LG, but their site is unhelpful and their phone line is currently closed.
On practical basis there are basically only a handful of companies that are the OEMs and make the multitudes of notebooks out there for all the notebook sellers, so a “genuine” power supply is relative term WRT notebooks as most adapters are sourced out the same handful of Chinese companies and often come from the same company whether generic or manufacturer direct.
If you cant find the specific adapter you want this one would probably accommodate your needs.
Am I understanding then that the amps (what I assume “A” stands for in “3.5A”) aren’t important, just the volts(what I assume the “V” in “18.5V” stands for)?
Well, they’re important in that the power supply must be able to supply the demand of the device in question. If your device draws 2 A but your power supply can only supply 1 A, then you’ll probably wind up burning up the PS, and possibly damaging the device. OTOH, if the PS can supply 5 A, the same device will still only draw 2 A and everyone will be happy. Note that this only applies to regulated power supplies (which includes all switched-mode supplies, such as nearly any laptop PS); unregulated power supplies only supply the voltage listed when run at the rated current draw. For smaller draws, the voltage will be higher–how much higher depends on the regulation factor of the transformer. Good (read: expensive) transformers won’t vary too greatly, while cheap ones will usually suffer quite a large variance.
The rating for the amps is important as a minimum. Whatever power supply you use must be capable of supplying at least the amperage required, but if it is rated for more amperage, the device will draw only what it needs.
The only drawback to getting a power supply with a higher amperage rating than required is that it may be larger and cost more. Operationally there should be no downside.
On edit: What Q.E.D. said.
So, to answer the second part of my question, I would not be able to use the power supply from my other old laptop because while it supplies enough amps (4.5 vs the 3.5 the laptop wants), the volts it supplies (16) are not sufficient for what the laptop wants (18.5). Right? (IOW, a little over on V and A is fine, but under is not)
For the specific purposes of what you intend to do, yes. As a side note you might want to double check the PS output with a volt meter before deciding it is the problem and not the notebook. Also if the fault is in the connection plug and not the PS brick Radio Shack does sell replacement coaxial power plugs. although they do require soldering.
Generally speaking, you want the voltage to be dead on, and the amps at least the minimum required.
A little over or under on the voltage may not hurt, depending on how good the regulation is on the laptop, but it’s hard to say with certainty without knowing the technical specs of the laptop. Having said that, a half a volt error on top of 18 is probably pretty safe. But supplying only 16 volts where 18 is called for is likely to cause problems, possibly both with the laptop and the power supply.
Also make sure you match the output type, AC or DC.
And as others mentioned, you also need to match the plug that connects to the laptop. And not just the shape, but if the power supply output is DC, (most are, I think), also the polarity. Polarity determines which of the two conductors is positive, and which negative.
The end of the power cord adapter is crushed into two pieces. We certainly do need a new one.
For the sake of thoroughness, I’d like to point out that it’s possible to damage an electronic device by using an unregulated power converter that has the correct voltage rating but too high a current rating - e.g. unit wants 14v @2A, you attach a converter rated 14v @10A - poof.
The problem is the way these transformers are rated. The unregulated ones are rated X volts AT Y Amps. However, the unloaded (or lightly-loaded) voltage may be much higher. Regulated power supplies won’t have this problem, but simple “wall wart” transformers will.
I know this because I’ve smoked things this way…
You don’t say? 
Your cheapest and best solution would be to get a replacement for the broken end of the power cord at Radio Shack, cut off the broken end and wire on the new one. Then you know the voltage and current specs match exactly. Just make sure you get the polarity correct.
Good luck with that. These days they tend to be proprietary multi-pin connectors.
I just replaced my power supply this past weekend (lucky me, I found a guy selling the exact part on ebay, and he lived across the river and sold it to me in person for 30$ rather than the 70$+shipping I found everywhere else! yay!)
A lot of people who repair/build laptops sell pieces on ebay, I’d definitely look there to see if an original part is available. Your power supply box will probably have a series/model number on it, and you can use that to google the part along with your laptop model. Mine actually had a number for the part AND a recommended alternative to replace it with, which came in very handy since the new one is an alternate (but still an hp/compaq original).
Take the laptop and the mashed adaptor over to Baynesville Electronics on Joppa Road. They are a block or so west of Loch Raven. They have a much wider selection of stuff than Rad Shack, and the folks there seem to be on their game.
That was Dave’s first thought.