Your first step, before you do anything else, should be to call a registered piano technician to inspect and tune the instrument. Based on what you’ve said, he may be able to repair the broken hammers on the spot and put the instrument into basically playable condition. He will also be able to advise you on additional work that would be needed and give you an estimate. The initial visit will probably cost about $100-$150.
Two of the most important factors in determining the quality of an older piano are the sound board and the pin block. If the sound board is cracked the tone may be affected, although it’s not always a fatal problem. However, the pin block is much more important. It is the piece of wood into which the tuning pegs are driven. A crack in it can keep the instrument from ever being able to hold a tuning. There are ways to repair a pin block that is not too badly cracked, but they are generally unsatisfactory. A cracked pin block is usually the kiss of death. Your technician will be able determine the condition of the sound board and pin block, and many other important points. (You won’t be able to do this on your own.)
Assuming it passes on these and other critical points, it is highly likely that the action will need to be rebuilt. This is a task that the technician can do in his shop, without moving the piano out of your house. (The action lifts out as a single piece.) He will repair and replace worn and broken parts, including the hundreds of felt, leather, wood, and cork bits and pieces. It can take a few weeks and cost a thousand or two, but once it’s done your instrument will play as well and sound about as good as it can.
As for the outward appearance, your technician can also advise you about refinishing the casework and make suggestions about what you might do yourself, and what you’re better off having done professionally.
However it’s possible, even likely, that this piano is not worth the $2,000 - $4,000 that might be spent in restoring it internally and externally. As you’ve found in your Googling, the brand is quite obscure, and that’s usually bad news with an instrument this old. (It is apparently pre-1900.) The famous names (Steinway, Baldwin, etc.) are often worth restoring, but more obscure brands usually aren’t, at least in terms of someday recouping the money you’ve spent on it.
But that’s not the only consideration. If this piano has serious sentimental value to you and plan to keep it, but can’t spend a fortune, you might simply restore the outside so it looks nice, without making it really playable. Conversely, if you just want something to play, you could make it sound good (as good as it can) without worrying about the looks.
But if it doesn’t really matter to you that it was dear Aunt Sadie’s piano, and are just interested in having a good sounding, nice looking piano to play or learn on, your best bet might be to junk this one and buy a different instrument altogether. Chances are that for less than $1,000 you could find an old upright from the '20s or '30s that would sound and play better that this one ever will. Or for about $4,000 - $5,000 you could buy a used modern upright (I’m partial to Yamaha, myself) that will be far superior in tone and play than your legacy, no matter what you spend on it.
You can discuss all of these options with your technician, and he can probably give you a line on those alternative instruments, too, if you decide go that route.
If you’re really serious about learning more about pianos, I highly recommend Larry Fine’s “The Piano Book.” (You don’t need to buy the supplement, which provides additional detail about various brands: neither C.A. Smith nor any of its successor companies are listed, at least not in the 1999-2000 edition that I have.)
BTW, you don’t need carbon tetrachloride to clean the keys: Windex, Formula 409, or a little soapy water will work just fine. And clean the outside, if you want, but apart from vaccuuming dust out of the bottom, I’d suggest you not attempt to clean the innards. Not worth the possible damage you might do.