All this talk about chipsets makes me thinke the following thoughts:
You can't buy a 'new chipset' - it's soldered permanently onto the motherboard.
Compaq stock CPU? Compaq doesn't make CPU's. Intel, AMD and a few others do. If you have upgraded the stock cpu with a Celeron, my guess would be that the ctock cpu is an intel. Now for the upgrade-bit: if you've upgraded the cpu, are you 100% sure the motherboard supports that new - and most likely considerably faster - cpu in the first place???
Next thought along the 'Compaq-PC'-line: Compaq PC's - as well as IBM's, Dell's and all the other brand-name-PC's out there have given med bad upgrade-experiences all the way.
My number one reason for NOT buying brand-name-pre-assembled PC's is the fact that they're not very upgradable. Manufacturer doesn't want you to be able to lifespan-extend the machines - he'd rather you bought new ones. More earnings and less hassle (warranty etc.).
To put things in perspective, a new motherboard can be bought in my local computerstore for approximately the same amount of money ten BigMacs cost. 40 Euro - or 300 danish 'kroner'. Approximating pocket change...
You get: a new chipset, an onboard VGA, a LANport, soundcard and a few other basic features. Follow this link for proof: http://www.shg.dk/link.asp?goto=infobox&varenr=310664
- An ASRock motherboard carrying 'Varenr 310664' will set you back 289 kroner.
Your Compaq cabinet most likely will not accept this motherboard. Tough luck.
Brand name PC's have a bad reputation for being picky with RAM as well.
So i'd suggest you try this:
Replace your upgrade cpu with the stock cpu. Remove any additional RAM you added. Use only what was in the machine when you got it. As for the chipset, i'd have no worries. The upside of having a brand name PC is that it's usually VERY stable if you don't try tweaking it. (The inner logic in this postulate is that brand name manufacturers sell gear to end users who will return any and all malfunctioning machines for RMA. They wil actually USE their guarantee, and manufacturers don't like throwing money back at consumers. Besides that, they have a reputation to uphold.)
This will cost you nothing at all.
I believe you have a hardware issue. To resolve it, i suggest you revert back to 'known good' - being stock cpu and RAM according to manufacturers specs. As far back as you can go. And remove any expansion cards, too. I once had a brand name TV-card that made my machine go bonkers. Wacko! Random reboots and freezes. Worked fine in another machine. Sold it, bought the cheapest noname-card i could possibly find - works like a charm.
If reverting back to basics gets you in the air, try adding stuff back to the system. Locate the offending component. Either live without it or replace it with something that works.
This, assuming you want to avoid spending money on the project.
Now, knowing you have seen and made working systems (using other people's hardware), we can agree on the fact that it's just *your* hardware that isn't behaving. Right.
So you'll either have to fix it or get new, depending on what is most important to you.
If knowing WHY it doesn't work is most important - fix it.
If getting on with the project is most important - my advice would be to buy the cheapest cabinet and a similar (cheapest!) motherboard to go with it, then transfer your Celeron, the RAM, disks, optical drives and floppy drives to this new 'home'. OK, this ElCheapo cabinet will be noisy, and you'll most likely have a hard time finding a motherboard that accepts your Celeron AND accepts your ram AND has a reasonable onboard vga/lan AND is really cheap.
But you will be free. Free to choose a motherboard. Free to choose a VGA card. Free to tinker with all the stuff on the market. Going all component-crazy is no bad thing. Motherboards must be compatible - otherwise people won't buy them. RAM must be compatible - same reason. Graphics cards must not only be compatible, they must have proper driver support and be cheap, because there's a war going on in this market segment.
Assuming all your stuff can be moved, this operation may cost less than 70 Euro. Less than you pay for 17 BigMacs.
Success isn't guaranteed. But close...
Note on heatsink 'grease': This compound is NOT lubricant. It's intended to improve thermal contact between CPU and heatsink, and adding MORE is a bad idea. Less is better - unless you use too little. Then THAT will be bad. Choosing the right amount of thermal compound is something of an art. But most people use waaaay too much 'just to be sure'.
First, ONLY the contact surface between CPU and heatsink must contain compound. Athlon/Duron CPU's have capacitors onboard. these must be clean and dry. Same thing goes for the green PCB sarrying the CPU core. Clean. Dunno about Celerons. But keep it clean.
Second, having smeared some compound onto your CPU core, you should be able to read the lettering on the surface through the compound layer. If you can't, IMHO you have applied way too much.
And another thing; many heatsinks come preconfigured with a 'heatsink compound tape'.
IMHO this tape is usable one time only. If you remove the heatsink, remove the tape and replace it with compound. It will require some work on your part.