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:
We have a Westell B90 modem from Verizon and a Netgear WGR 614 router on the main computer. The ethernet connection on the modem is quircky--if I get near it, it stops working and we can't get on line. Verizon sent an incorrect replacement long ago and now tells us just to get a new cable. The connection seems loose. Also, the other desktop on the network always gets a low signal. It is on the same floor in another room, but with open doorways. The new lap top gets a very good to excellent connection on the next floor up.
Would a new antenna for the 2nd desktop help? Netgear says the router and the card are OK because they work. It takes so long to get help at Verizon so we hesitate calling. Would a new cable help or do you think the problem could be in the modem?
Thanks for any suggestions.