Troubleshooting for a PC that does power up, but does not post.
A PC that doesn't POST is only one step better than a PC that doesn't power up, so when a PC doesn't POST, you want to follow the same rules as troubleshooting a PC that doesn't power, except for the testing of the power supply and the placement of the power switch. Pull all of the cables, pull all of the cards except for the video card and if something still doesn't come up on screen, you at least know that the problem is either the video card, the RAM, the CPU, the motherboard or power supply and not some flaky modem or IDE cable.
One common misconception I hear a lot is that because one doesn't have video on one's monitor, one must have a bad video card. This is not always the case. Remember that getting video to the monitor is only the end result of everything else working properly.
Let's assume that you currently have the PC stripped down to just a power supply, motherboard, CPU (with a fan on it of course), memory and a video card like I had asked in the first paragraph. Now, a POST signal goes through the system in the exact order that I just listed. If the machine is at least "trying" to POST, then we should get a response of some sort with what we have here.
First, power up what you have and look at the monitor. Nothing? Do you hear any beeps? Make sure that you not only have a speaker plugged into the front panel connectors of the board, but also in the back of the motherboard if your board has on board sound (sometimes POST codes go through the on board sound chip). No beeps still? Let's start...
The first thing to look at is the dip switches and/or jumpers on the motherboard. Most boards, if you do not set the dips or jumpers, should POST right out of the box. In some occasions, the front side bus may be "too high" (for example: Set to 133/266 for a 100/200 MHz FSB Athlon or Duron or set to 133 for a 66 MHz FSB Celeron) and this will keep the PC from going to POST. If you think this may be the case, check the manual and see where these "should" be set. UPDATE: Motherboards have not had front side bus dips or jumpers since the introduction of the Athlon64 or Pentium 4.
When things still aren't going your way, the first thing to pull is the video card. Obviously you won't get a picture if you do this, but we should at least get a beep. Typically the beep is a staggered beep going from one long beep to three short beeps (however, this may vary based on who made the BIOS program, so check with your manual). If you pull the card and you get a beep, then your problem is either a bad or incompatible video card, or there's something up with your monitor. Have these parts checked!
If you still don't get a beep, it's time to pull the memory. If you pull the memory and fire up the PC, you should get beeps. Usually the beep code that one gets when there is no memory in a PC consists of the same tone over and over again, but sometimes can beep in sets of three (AMI BIOS). If you pull this RAM and get a beep, then your no-POST problem may be RAM related. If the PC still doesn't beep, we have an issue on our hands and it's probably time to call the folks you got the motherboard or CPU from. You see; at this point, you should only have a CPU and a motherboard hooked up to a power supply. Fact is, if you had a working power supply, motherboard and CPU and you fired it up, you should at least get a series of beeps.