Since it is beeping and not crashing (and from what you have told us it is the little mobo speaker that beeps, not the sound card) I'd suspect a CPU overheat warning.
When you put the CPU cooler back after you replaced the heat sink paste, did you put it back in the correct orientation? It is possible to put the Athlon XP coolers back 180deg out. There is a step in the cooler which, if you get it wrong, actually prevents the cooler from making proper thermal contact with the CPU.
Suggest you check this.
As for the bootup beep error-codes - from the manual for your mobo -
http://download.gigabyte.us/FileList...n400pro2_e.pdf
AMI BIOS Beep Codes
*Computer gives 1 short beep when system boots successfully.
*Except for beep code 8, these codes are always fatal.
1 beep Refresh failure
2 beeps Parity error
3 beeps Base 64K memory failure
4 beeps Timer not operational
5 beeps Processor error
6 beeps 8042 - gate A20 failure
7 beeps Processor exception interrupt error
8 beeps Display memory read/write failure
9 beeps ROM checksum error
AWARD BIOS Beep Codes
1 short: System boots successfully
2 short: CMOS setting error
1 long 1 short: DRAM or M/B error
1 long 2 short: Monitor or display card error
1 long 3 short: Keyboard error
1 long 9 short: BIOS ROM error
Continuous long beeps: DRAM error
Continuous short beeps: Power error
10 beeps CMOS shutdown register read/write error
11 beeps Cache memory bad
A hard memory error when up and running will almost always crash the system (and you'd better hope it does before it corrupts stuff).
Otherwise try Memtest86 -
Memtest86+ - Advanced Memory Diagnostic Tool
Finally, 1GB is barely enough for WinXP - you could try and find a couple of matching 1GB sticks of DDR400.
Good luck!
Mac