I had a similar problem, and it was fixed by a technician who just pulled out the RAM, the hard drive, and keyboard and then put it back in again and it then started working. The symptoms were that I hit the power button, with or without the AC adaptor plugged in, it would blink green lights twice, and then immediately power off. It sounded like it was powering on, but there was no screen (just shut off).
Of course, if I had followed the advice from the FAQ to just take everything out one at a time that would have fixed it (see Latitude Power management FAQ).
Well good luck.