Hello, I have recently had the same problem trying to revive an old machine. At first, as soon as I would power it on, the fans spin about once and then shut off while the power light would blink continuously and regular intervals. I checked the fan on the back of the PSU, and it was running, but I went ahead and replaced it with on from newegg to be sure. 3 days later and with a new PSU, the computer still will not post, however, the power light went from blinking to a solid light. Because this the case, I promptly checked the processor, which was shockingly seated wrong. I reseated it with the gold arrows pointing in the right direction and applied fresh thermal grease before replacing the heatsink. Now that that has been accomplished, powering on resulted in a full post, however the initialization of the boot process would freeze in random moments, rebooting it self, even while in the bios. This seemed like a memory issue, and so I proceeded to check the ram. This rig is an emachines, and it included 2x 512mb of ram from hynix, rated at 400 mhz and I had previously booted with only one stick in. My first theory was that perhaps the computer needed both sticks as in the stock configuration to work. To my surprise, placing both sticks in resulted in glitches in the screen and even more frequent freezes. Luckily I had several unmarked ram sticks lying around, and proceeded to test them out. One stick from kingston would prevent the computer from posting, resulting in a long pitched beep continually. I next tried a samsung 128mb stick rated at 333mhz, and the computer followed through post and didn't freeze, and completed a test run of an ubuntu live cd with no errors.
Summing matters up, there was something wrong with the PSU in the beginning to cause the power light to blink, even though the fan still ran on it. Next, with the power light fully on, I checked the processor which was seated wrongly by the previous owner which kept the system from posting. With now a full post, I have discovered that the original memory sticks were corrupted, and so replacing them with the correct frequency successfully lead to a revival of a thrown away machine. Further notes: be sure to check the Clear CMOS jumper to see if it has a 2 pin connector over 2 of the 3 pins, and to make sure it is in the correct location. It would also be a good idea to check/replace the CMOS battery before trying to diagnose the processor.
I have done the same to another machine (ironically another emachines..), but while checking the processor, I find that it will still not post. It is a 478 pin cpu, whereby I tried both the stock celeron 1.7ghz and a celeron D 2.5ghz processor, where both would not initiate a post, so in this case I would have to replace the motherboard.
I hope some of these steps I used to diagnose my machines will be able to help some of the many people with computers that will not start. I am gladly going to wal-mart today to purchase another keyboard for this new rig now. Another note, please don't tinker with any delicate components within unless you are confident or are aware of the consequences. It is very thrilling to be able to fix an old computer, but should it be your only computer or have significant value placed within it it is better to take it to a professional. They will be able to better diagnose the situation and give you a more accurate solution to any problem you may face. One must be aware that by trying to do good can inadvertently cause more harm in the end.
regards.
~fain