I have a bunch of coax in my house. I just finished a remodel of a
room in my house and the cable that runs into that room produces fuzzy
channels only on the low channels (< 20). I  have tried a signal
amplifier (5-450mhz) with very little improvement, if any. It is the
only room in the house affected this way, but was fine before. I ahve
tried two different tvs int the room, with the same result, and have
bypassed the wallplate. I have broadband cable with a Motorola
surfboad modem, if that makes nay difference. No grounding is evident
on the coax runs.

Bad cable 
- or it is running over a power line, preferably at 90 degrees

Do a run over the carpet and see whether it still fuzzes.

You have terminated the connectors correctly? No screen whiskers
shorting out? If in doubt, do an unconnected test with a digimeter.
Should be open circuit between inner and outer. Then short the inner
and outer at one end and check that the other end measures this short.

Best

Should also have added that one of the main causes of co-ax failure is
carpet tacks shorting the inner to the outer. Can really screw up your
mates too with a pin through their cable.

Best