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mmts 
You've made things pretty easy by providing a link to your system's original specs, and I see it uses PC100 memory. These days it's not so easy to find boards that will accept PC100 memory modules, so let me propose two routes you could take: re-using the PC100, or upgrading to some DDR PC2100 memory.
To get started:
archived thread listing some online stores in Canada
Next, the bad news up front: your computer has a skimpy 185-watt power supply.

I may be one of the most conservative people around here when it comes to power supplies, but I'm laying good odds that a 185W power supply is going to be hard-pressed to keep your system stable when the Radeon 9600XT is factored in. ATI recommends 300W+ power supplies for systems that will have their upper-end cards in them. So I would counsel you to bail on the HP case & power supply at the same time as the motherboard, and get a case with a respected-brand power supply such as an Antec, Enermax, Sparkle Power, Powerman or even Enlight. Inwin's S-series mid-towers, Enlight's 7000-series mid-towers or Antec's mid-towers all come with PSUs that at least live up to their ratings, if not exceed them. Think it over.
Re-using the existing PC100 For this purpose, look for a store that has a KM266 or KM266A motherboard with SDR memory slots. Here's one from British Columbia:
MSI KM2M Combo-L, which has slots for PC100/PC133 as well as slots for DDR modules. I know it only has an AGP 4X slot, but that is compatible with AGP 8X cards. The performance difference between 4X and 8X modes is difficult to measure even using benchmarks, much less real life, so don't stress about that.
This motherboard is only CA$76, leaving you some funds towards a decent case & power supply like
this one. Antec has less-expensive models starting at CA$70 that feature their SL300
S power supply, but it has a single sleeve-bearing fan where the models featuring the SL350 power supply have dual ball-bearing fans and 50W more power. Down the road, I think the extra power and the better fans may be worth the extra money, but it's your call.
Upgrading to DDR memory For this route, the excellent CA$86
Asus A7N266-VM/AA motherboard and some Crucial PC2100 DDR is a good match for your Tbird. The board also has the finest onboard audio in existence, complete with both optical and coaxial S/PDIF outputs so you can pipe Dolby AC3 digital 6-channel audio straight to your home-theatre system if you want. This onboard audio is typically compared to Creative Labs' original Audigy card in both performance and quality. I have a lot of experience with the A7N266-VM/AA because we use them at work. Very nice boards.
Either way, if you are planning to play games that will truly give the Radeon 9600XT a workout, you'll probably benefit from upgrading to at least 512MB of RAM when you can afford to, and a faster CPU wouldn't hurt either. Hope that helps!
edit: having shoehorned an aftermarket microATX motherboard into an HP case before, I also want to mention this: it may not work without some creativity!

I had to remove the retaining clip off one end of the memory slots on the board that I used, that's how tight it was in there. Also, I had to get creative with the case's block of power/reset/LED wires... another pair of reasons to get a new industry-standard ATX case while you're at it.