The router's pretty old, and I can't replace it. I might just get a new router/internet connection for myself and be done with it.
The older the better, actually. Once Cisco (Linksys) realized how popular firmware replacement was, they started to limit the onboard memory to make it more difficult, and selling another version with more memory at a higher price. So the older ones usually are the easiest ones to flash the firmware on, as they normally came with 8+MB of flash rather than the current standard of 2MB. What's the model? It's most likely a WRT54G, so look for a version number as well.