Compaq Presario v2000 mouse/keyboard SOMETIMES working

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Yeah, it seems like your Notebook is dying. Here's a few things to try:
Software:
1. Run MSCONFIG -> select Diagnostic
2. Clean the fans and other parts: get a canister of compressed air and blow-out the dust.
3. If the registry is mildly corrupted then first run CCleaner Registry tab -> http://www.piriform.com/ccleaner
4. Scan for Malware and Viruses: Use ESET online scanner -> http://www.eset.com/us/online-scanner
5. If the HDD is filled-up then use Windows Disk Clean Up.
6. System File Checker and HDD Scan - Click My Computer / right-click Local Disk C: / select Properties / Tools tab / click Check Now / select both options then Start / Restart. Process takes ~20+ minutes to complete.
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Drivers:
1. Open the Device Manager, Expand the [+] Mice... right-click Delete and using the Keyboard Restart; this will disable temporarily the Trackpad until the restart is completed. However, it will reinstall the Driver(s) and fix corruption. You might want to do this procedure on the [+] USB...
2. Update your Drivers http://h20000.www2.hp.com/bizsupport/TechSupport/Produc...

Above is a good starting point.

I can't get the mouse/keyboard working long enough to do anything really on the software side of things.

The compressed air idea might do something, that's a good idea. I'll try it later this week

Do the drivers you mention extend only to Windows? Because this isn't an OS problem, I tried installing Linux and the same freezing symptoms appear DURING installation.

It's so frustrating, everything technically WORKS at one point or another, but it can't even be used!

If they work and suddenly start not working then my assumption, short of a failing MOBO, is an over heating problem <or> corrupted BIOS/CMOS Battery.

Therefore, the cleaning and new CMOS Battery would be my best recommendations. Replacing a CMOS Battery on a Notebook is a bear unless it's conveniently located; this in most instances needs to be done at a repair center. I've yanked apart 3 notebooks and you need to be REALLY CAREFUL!!!

The remainder of my above info is 'Good House Keeping' and I'd do it anyway.

Good Luck - Let me know!

CMOS battery? You think that could cause the mouse/keyboard to die after about a minute of use?

I took it apart already, ha. I swapped out the heat sinks and screens from an even more broken computer of the same model. I'm not sure where the CMOS battery is, but I'll look into it and see if that will work

A bad CMOS battery does and can do all sorts of bizarre things, and if your Notebook is >5 years old chances are it needs to be replaced. --no guarantees.

It too might be worth while to flash the BIOS. Based upon above: Bad MOBO or Bad BIOS incl Flash/Battery are all possibilities.

Well this is the weirdest situation ever.

I went to hp.com and compaq.com and VERIFIED that the computer model's BIOS was for my computer, and the latest version was F.23A
When the version that my computer BIOS says is F.27

I put the F.23A on a CD anyway, and by some miracle lasted long enough to boot in and try loading it

NOT the right BIOS for my notebook, it says. Now that's just baffling.

Also, I left my computer in a very cold room and booted it, the mouse/keyboard worked for about two minutes, which is like twice as long as I've ever seen it work.
I was able to connect to my wireless router, type ipconfig in CMD hoping to maybe do remote access on it, and even load up google.com in IE before the mouse gave out.

Cold = longer life. Sounds like possible overheating problem? Except... wouldn't that cause it to turn off?

Any insights?

Yeah, the second item above was "Clean the fans and other parts: get a canister of compressed air and blow-out the dust. " -- hoping dust is blocking the cooling. You might also have a bad CPU FAN. If it isn't spinning the it takes only moments for the PC to become unstable and shut-down.

What you described seemed like overheating.