here is how I would troubleshoot this:
1) get a multi-meter with digital readout. There are inexpensive ones avalaible for less than $20 and is a good thing to have.
2) test the DC voltage at the amp (right on the terminals) between the +12V power wire from the battery and the ground cable. Engine and system can be off for this. If you get about 12.0-12.9 volts here, then the main power supply to the amps is fine. If less, then either there is a blown fuse in the power supply somewhere or you have a bad ground.
3) test the DC voltage at the amp (right on the terminals) between the remote turn on lead from the head unit and the ground cable. The system must be on for this. If you get about 12.0-12.9 volts here, then the remote turn on to the amps is fine. If less, then need to determine if there is a fuse on the turn-on lead (sometimes there is, but usually not) or id the deck output is not working (repeat test close to connections at rear of deck).
If the power from the battery and the turn on from the deck are fine, but the amp still does not power up, then check for any internal fuses that may have blown. I am not familiar with the Eclipse amps to know if there are any.
You mentioned a red light on the amp... it may be in protect mode. Again, I'm not familiar enough with eclipse to know, but the dealer in town should be.
There are more troubleshooting steps to take, but I'll wait to see if any of these work first.
