I have internet service through time warner cable. The modem works for five days then shuts off (just two lights blinking) for four hours and comes back on just as though it was on a timer. The cable company said it's probably a power supply problem and to get a surge protector. Does that sound right?

No it sounds like an excuse...
Don't call anymore...
Unhook it, unplug it.. and carry it into one of the Time Warner locations (make sure they are open first before you go)

Tell then something is wrong with it and you want to swap it.. they will do it - no questions asked. I have done this with modems and cable boxes . :)