Motherboard/Video Card Upgrade on a Budget - Need Help

Hi, sorry if this isn't the best place to put this.

I am currently looking to upgrade my system (mainly the motherboard and video card), but I'm on a bit of a budget and I need some help deciding what would be best to get and what is compatible with what.
I am mainly doing this because my graphics card is starting to go and I was told that if I want to upgrade my video card, I should go with PCI_Express, but my motherboard does not suppport it.

I mainly like to play First Person Shooters (not necessarily to their fullest graphical potential), RTS and WoW

My friend helped me build this system a few years ago, so I don't know exactly what I am doing.
So, any feedback would be much appreciated

Here is a summary of my PC details (pulled using Belarc Advisor)
If you need any more info, just let me know and I will try to get it

Thanks =)

Processor:
2.80 gigahertz Intel Pentium 4
8 kilobyte primary memory cache
512 kilobyte secondary memory cache

Main Circuit Board:
Board: ASUSTeK Computer Inc. P4P800SE Rev 2.xx
Bus Clock: 200 megahertz
BIOS: American Megatrends Inc. 080009 03/15/2004

Memory Modules:
024 Megabytes Installed Memory

Slot 'DIMM0' has 512 MB
Slot 'DIMM1' is Empty
Slot 'DIMM2' has 512 MB
Slot 'DIMM3' is Empty

Power Supply:
Wattage: 300W
Model Number: AP-350X

Display:
NVIDIA GeForce FX 5500 [Display adapter]
Samsung SyncMaster [Monitor] (19.1"vis, s/n H9NLC05448, December 2006)

Thanks for the response =)
Do you have any recommendations on a decent motherboard that supports pci-e that is relatively inexpensive?

On a side note, would it be the power supply causing my system to shut off whenever I use my DVD burner for anything? (my DVD Rom works fine without this issue) if so, I would need to replace it anyways.