By way of comparison, I ran the following system as my HTPC for 7 years of moderate use with no issues whatsoever:
ABIT KV85 Socket 754 motherboard
Sparkle 270W PSU
Athlon 64 3400+ Venice (2.4ghz)
Thermaltake Venus 7+ CPU Cooler
1GB Crucial RAM (Two 512MB sticks)
Radeon 9600XT AGP
Two IDE hard drives
One IDE DVDRW
One PCI WiFi adapter
One PCI ATI HDTV Wonder
One PCI Chaintech AV-710 sound card
Two 60mm rear fans
One 80mm front fan
Please consider:
My Sparkle 270W PSU is probably comparable to your Enlight 230W PSU.
I was running two IDE hard drives, three PCI cards, and a 9600XT.
I assume that your 2400+ and my 3400+ consume about the same amount of power.
Your 9600 will consume only 15W, max. My 9600XT consumed only about 25W, max.
The old 9600 series Radeons were very low power and low heat video cards. However, they provided a pretty good level of performance. They were perfect for HTPCs (circa 2006), in my opinion. In fact, I removed the HSF from mine and installed a totally silent Zalman ZM50-HP passive cooler. I never had any problems.
I think you're gonna be just fine with the system you have. You can probably upgrade to a 9600XT without problems, but I wouldn't push things beyond that.
If you have problems, you know that your PSU is the first place to start troubleshooting. In that case, you should swap with your spare 370W PSU to see what happens. If you need a new one, Rosewill makes a pretty nice 350W PSU with a strong 5V rail for your Athlon XP for about $30. I use one in another box of mine that runs an Athlon 1400 and Voodoo 5. I have no complaints and would recommend it if you have problems.