Make sure that the problem is not radio interference.
Is there a way to know if wired connections to the same router are still happy while the wireless connection is down?
Most routers come set for channel 6 out of the box. Most folks who change this go for either 1 or 11, to distance themselves from the rest of the crowd.
You can use a freeware wifi detection app to see what different wireless networks are running in your area, their signal strength, and their channels.
Note that devices such as microwave ovens do affect wifi.
About replacing the router…
What kind of Internet service do you have (cable, satellite, dsl)?
Is there another box between your current router and the service entry point in your home?
Some ISPs provide a company-branded device that contains modem + firewall + switch + wireless access point. If yours is one of these, then you cannot just replace it with your own device. You would need to talk to the ISP and see if they could provide a new box.
With such a all-in-one box, you can piggyback your own wifi router on top of it, but there are network details you would need to iron out.
I am firmly against the “hide SSID + use MAC filtering” point of view, FWIW. These are the flimsiest excuse for security and all they do is make your own life harder, while giving you a false sense of security.
As you pointed out, hiding the SSID made it difficult to configure your other devices. Indeed, I have some devices at home that won’t find the network at all unless the SSID is turned on at least for a moment.
Networking problems are challenging enough to figure out, so it makes it easier if you eliminate unneeded complexities. Imagine sending your computer to the shop for repair and then wasting four hours trying to figure why you couldn’t connect to the Internet, not considering that the new network card they swapped in would have a different MAC address?
Besides, the SSID broadcast allows you to send cute, passive-aggressive messages to your neighbors.