go on ebay and buy a 20 foot Ethernet cable and test it.. In my house my router is in my living room so I have an Ethernet cable go from router to outside..it trails up to the loft and out the other side and down into my room and the cable cost me £10 from ebay.. All I did was follow existing wiring for the tv aerial etc so it don't look messy, That way you can test your pc/laptop in your room with a proper connection and it cost you under $20
Wireless is rather fickle, even with a newer, better wireless router it still might not work, depending on lots of things. Does seem you found out what the issue is at least. Hardwired is better anyway. You can give the new wireless router a try, but I doubt Comcast will help you with it (AT&T and Verizon won't) unless you go for some paid premium support.
actually some companies here in the US have started charging a rental fee on the modem. buy your own and your monthly is 4 cheaper. if the modem lasts it pays for its self over time
@OP
you can either buy a new modem/router or try and get them to replace your modem/router..
threaten to switch companies if they dont replace the modem if necessary.. even if its an empty threat should work.