General Diagnostics

When a computer crashes there are many possible problems, each with different solutions, but it is useful to be able to quickly recognize what type of problem you are facing.
The first step is to determine if the problem is with hardware (a physical part of the computer), of software (programming, operating system, etc.) based. Often these problems both manifest themselves the same way so it can get a little sticky deciding what's wrong. You don't want to start spending money and replacing parts only to find out that the problem was with the software, of course after you've reinstalled an entire operating system and find the problem is still there makes you wish you had just replaced the broken part. Laptops can also present their own set of problems since they have more hardware components than a traditional desktop that are very difficult to change out or check.

First, little glitches like a program crashing is usually software. Pay special attention and try and recreate the problem. If you know what causes the crash, then you can usually fix the problem by removing or reinstalling the problematic program.

If a computer crashes and will not turn on.
Pushing the power button does nothing, and you are certain that it is all plugged in and has power then you are probably looking at a power supply issue.
If when you push the power button it acts like it is turning on, you hear some noise, and some lights flash, but nothing shows up on the screen the computer promptly turns back off then you are probably looking at a logic board problem.
A laptop acts like it is starting up and everything seems right but you see nothing on the screen you either have a bad display, or you settings are set to use an external monitor. Try plugging in an external monitor to see if you get an image. Sometimes the display will be bad, but the laptop will still work with an external monitor.

If a computer starts up but gives errors during startup that prevent the computer from starting. Sometimes the computer will tell you the problem and sometimes it just freezes.
This is when it gets a little hairy. You might have ram problems, a hard drive failure, or something wrong with the operating system. Pull out one ram module and try the start-up again. Replace the ram and pull out the next until you have tried starting up with each one out. If one is bad then the computer will work with the bad module out, but not with it in.
If RAM is not the problem then see if you can boot into safe mode. Press F8, F10, or F11 when the computer starts up. You are trying to get into the boot menu. If you can do this choose safe mode and see what you get. If it starts up in this mode you either have a bad peripheral or the system is stuck in normal start-up. Try a System Restoreby going to Start- All Programs- Accessories- System Tools- System Recovery. Choose the most recent recovery point and follow the wizard. This will not destroy any data but it will downgrade some recent updates.
If this doesn't work then you probably have a more serious problem. You can try unplugging other devices within the computer, network card, video card, cd-drives, and see if any of these make a difference. Most computers don't have a lot of things to unplug, and usually the peripherals aren't causing you problems. You will need to run a complete system recovery. You do this by inserting you recovery or installation cd. Boot to it and choose System Recovery. You can often do this and not lose any data. It will take sometime, but is better then losing all of your data. Keep in mind that if the recovery process seems to work and doesn't give you any errors then your problem is not hardware. Even if in the end the computer still doesn't boot. Hardware problems usually prevent a recovery from even starting.
When a system recovery fails then it is time to try a clean install of the system. This will erase your data so hopefully you've backed everything up. If not, remove the hard-drive and stick it in a friends computer and back-up your data, then put it back and install the system.
Sometimes it will be necessary to erase everything on the drive before you can attempt an install. Doing a complete reformat of a hard drive can take some time but does fix some problems. I've seen computers that kept having errors even after a complete reinstall. By writing zeros to the drive and then reinstalling again the problem went away.
Good luck.