Being a good detective requires that you remember what an adverb is.  (hint- remember the who, when, what, where, days of grammar?)

Who Was the Last Person To Use the Computer?

Ask anyone with access when they used the computer last.  You'd be surprised how many people will confess that they got an error, didn't know what to do, and shut the power off.  In effect, they sub consciously didn't want to deal with it and handed it off to someone else.

When Did It Last Function Correctly?

Was it before the last service pack install?  Before a Windows Update?  Before the program Johnny brought home on a CD that a kid from school burned?

Was it after a fan started making noises?  After a power outage?  With wireless networks even microwaves and cordless telephones can cause problems.

What Was Done Between Then and Now?

Now that we know who used it last, it's time to find out what they were doing.

Did they shut down properly?  Did they download a program or driver?  Was it scanned for a virus?  Did it install correctly or give errors?  Did anyone try to properly uninstall a program?  Or remove it by deleting the folder it installed to, thereby removing files the registry or other system files are still trying to load?

What about e-mail?  It can contain malicious code or a virus.  Configure your system to send plain text mail.  Configure your e-mail client to open mail as plain text.  Make it a habit to not open html based e-mail from unknown senders or mail with attachments.

Did someone make a hardware change?  Was it moved or rearranged without unplugging cables, perhaps causing a cable to loosen, or even a card to get loosened from its slot?

Did they try to make some modifications that would magically enhance the computer?  There are plenty of valid tips to do things like speed your Internet connection, boot faster, shut-down better, and perform better in-between the startup and shutdown.  BUT, the proper 'tweak' for the proper system!!  A registry change that could enhance one version of Windows may bring another version to a screeching halt.

Where Did the Problem Signs Come From?

Now think, were there physical signs indicating a problem?  Use your senses!

Sight:  Did the monitor flash or flicker differently when powered up?  Was there an error message on the screen?

Sound:  Maybe a grinding sound when the computer first turned on indicating a CPU, power supply, or other cooling fan isn't working correctly causing overheating.  Is it giving a series of beeps that sound different than in the past?  Those beeps could be the BIOS telling you what is wrong, such as the video card being seated incorrectly.

Smell:  an electronic smell can indicate a heat problem.  Either it's too hot in the case or it's so dirty/dusty that dust is burning on contact with components.

Has it been properly maintained?

Has the operating system been kept up to date?  Microsoft is making it easier with automatic updates.  Is there anti-virus and anti-spyware software?  Have they been kept up to date and run regularly?  See the tune-up link listed in the Useful Links section.