Although the power supply on the 2600 is one of the most rugged ever built, banging any power adapter around usually causes it to fail. Test the power supply with a meter to see if its even putting out the right power.
Next, be sure you're using an RF in on your tv. If not buy an rf to composite adapter (likewise there's modding info on the net on how to convert your atari output permenantly).
Most likely cause though is the power switch itself. The switches are known for becoming "loose" over time. Look at the question about the broken switch and tighten/clean the power on/off switch.
While you're in there, locate the wire that goes out to your tv. It's a simple RCA wire plugged into the board next to the metal casing. Try subbing it out for a different rca wire.
Jiggle the wire where it connects to the tv. perhaps the push-on connector is loose. If you're still using the old switch box, then open that and clean it as well. They are also notorious for getting dirty over time.
Make sure there's nothing inside the cartridge slot keeping them from seating correctly.
Make sure slot pins and cart pins are clean.
Make sure you're on channel 2 or 3 (or is it 3 and 4, I forget). Make sure the channel selector switch is on one channel or the other, and not stuck half way in between.
Check all other switches for shorts.
If all else fails you've probably [like R5-D4 in Star Wars) "got a bad motivator unit", and should probably look for a new 2600. Before you throw yours out though, borrow someone elses and swap parts, see what works and what doesn't.