Oh boy - my boss brought me his kid's PC to see if I could figure out what's gone wrong. To challenge me even more, there are no CD's for it.

It's a Dell Dimension 8400. So far I've been able to check the HD using the built in utilities- no issues reported.

Cannot boot to anything - getting blue screen of death - STOP: 0x00000024 (0x00190203, 0x82b9d5e8, 0xc0000102, 0x00000000)

I found the first code (024) but cannot locate the rest of the error codes on line.

Since I don't have the CD, any suggestions?

I suggest you start by checking your hard drive.
Look HERE (http://www.techspot.com/vb/topic7602.html) for a list of hard drive diagnostic utilities.

Another very useful utility is the Ultimate boot disk. You can get it HERE. (http://www.ultimatebootcd.com/)

You might be able (just don't bank on it) to repair the drive using the utilities above.
Afterward, you will want to backup / ghost / clone the drive to recover all the data. (or all recoverable data).
Then, you may need to replace the drive, but you will need to evaluate the report from the drive diagnostics before this decision is made.

Once your data is backed up, you may be able to do a repair on the Windows installation (including NTFS).
Once you can boot (at least to safe mode) attaching some minidumps may help us do further diagnostics for you.

Should have mentioned, when booting via command prompt, it always kicks out at agpcpq.sys

I have a CD with that on it, but I can't force a boot to the CD for some reason. Changed boot sequence but keep getting Floppy error: floppy diskette seek failure, keyboard failure (deleted floppy out of sequence, same issue)

The computer has a panel of diagnostic lights.
Check this link for an explanation of the codes for the 8400
http://support.dell.com/support/edocs/systems/dim8400/SM/adtshoot.htm#wp1052387

From your description, I do not think you are getting any beep codes... (post codes).
Maybe the light codes will be helpful... (I suspect it will be yellow, green, green, yellow).

Update after further research... more information (re: agpcpq.sys)
You may wish to explore this, with special attention to post 18...
though other posts seem to have significant help as well.
http://www.techspot.com/vb/topic21511.html

Possible issues include
SP... is the machine running sp1, sp2, or sp3?
Is the machine running a fat32 or ntfs partition?
Do you have the latest bios update?
and Drive errors remain a significant possibility.

Thanks for the updates. I've researched th AGPCPQ articles, but there seem to be a multitude of reasons including both hardware and software.

Pulled the CMOS, started with it out, disabled hardware, started and let it rebuild.

Funny thing - I'm getting 4 green lights.