Inspiron 518 - intermittent power up, amber light blinks once and then stays off

I've read a bunch of other posts regarding power up issues but haven't seen one like this. I have an Inspiron 518 which  just started doing the following:

- When I put the PC into sleep mode, it shuts down rather than sleeping

- Sometimes, when I push the front panel button to power up, the light flashes amber once and then stays off. No blue light, no steady or flashing amber light, the PC doesn't power up, there are no diagnostic beeps, and the green power supply LED is on. If I press the power button repeatedly it eventually powers up.

It also seems that this only occurs when the PC has been powered off for some time. If I shut down and then power up soon after, it works fine.

My solution so far has just been to keep it on all the time, and not let it sleep (since sleep causes it to shut down). But something's obviously wrong and I'd like to figure it our before it fails completely.