Upgrading mobo and cpu

Hi, new here. I have an old hp amd athlon xp3000+. It's really old. I was thinking about upgrading the mobo and cpu while using reusing the hd, cd/dvd driver, power supply, and the actual hp case. My local micro center has the P5KPL-CM LGA 775 G31 mATX Motherboard and intel pentium e3300. I would also have to buy a ram stick or two for around $50. Cost would come around $150. I was also planning on the future to upgrade to a quad processor. I mainly use my computer to surf, music, and watching videos. I watch 450p and some 720p. My computer is also connected to a 32" tv. Is this worth upgrading? I'm a student on a real tight budget and was considering upgrading to a dual core processors.
Thanks

-edit-
Also how about a e5200 or e5300 processor? It has a mb more lc2 for $20 more.
Or should I go with amd? Amd mobo have hdmi built in and I really want to connect my pc to my tv via hdmi.

It's not really worth upgrading. To start, you'd need to upgrade to the current generation of sockets (AM3, LGA1156, LGA1366). The LGA775 is a dead socket. The AMD side wouldn't be too bad on the cost. You can get a good CPU and future proof board for about $160 (X3 425 and Gigabyte GA-770TA-UD3), but you'd need another $60 for a 2x1 GB kit of DDR3 RAM or $115 for a 2x2 GB kit (highly recommended). So it could be done for $220-335.

However, there is another problem. You said all of this is coming from an HP prebuilt PC right? The main problem with prebuilts is that the companies try their hardest to prevent upgrades. The PSU likely won't allow a new board, and the case may not allow for the standard mobo sizes.

Finally, the biggest problem to doing this on a budget: the OS. Prebuilt PCs use an OEM version of Windows that ties itself to each specific board. That means that if you replace the motherboard, you must replace Windows. And the OS isn't cheap. Right now, Win 7 Home Premium is $105. So add that to anything you want to do.

We could possibly put together the best PC you can get for what you're willing to spend if you listed out each part you have (specific model numbers or links to a vendor like Newegg). We also need to know if the resolution of the TV (full HD is 1920x1080). Since you're not a gamer, a completely new build would likely cost about $500 for the tower, plus another $100 for the OS.

DDR2 is the same price as DDR3 nowdays. There literally is no reason to stick to DDR2.