I'm guessing that this is a hardware manfunction of some sort.

After my computer has been on for a while it will lock up with no applications running. It will try to load an application but will appear to be using all available resources (hour glass on screen). In task manager, CPU usage is 0 and memory use is very low (<20%). It is working fine right now as I'm typing this, but will freeze up if the computer is left on for perhaps an hour.

After it freezes are there any diagnostics that I can do to check for a hardware problem? I'm thinking motherboard/capacitor, etc.

More info. When I say lock up, the mouse still works but applications will not open. I can get the Task Manager window to open from the keyboard (Ctrl-Alt-Delete) but if I attempt to open it form the bottom bar it will attempt but not open.

How about some specs for your machine.

How about mentioning which of the myriad of operating systems you're actually using. Saying "task manager" might infer Microsoft windows, but that's still too many to guess.

Is that "left on for an hour, but in constant use", or "left on for an hour displaying a screen saver".

My first thought is your HD has gone into sleep mode, and some buggy motherboard driver doesn't know how to wake it up again.

Dell Dimension 2400
XP home
I doesn't appear to matter whether the machine is in use or not. Even after a hard reboot (the only way to shut down when it happens) if the computer is still warm it will not open any applications.