From your description, it could be the cable, the router, or the cable modem that's causing problems, or it could even be something with your DSL provider.

One thing that would rule out your equipment is to temporarily attach your computer directly to the cable modem and see if the problem goes away. The next cheapest thing to try and replace is the cable between the router and the dsl modem. If that doesn't fix it, it could be the router.

For the wireless issue, you could try a wireless range extender like this one:
http://www.netgear.com/products/details/WGXB102.php