Hi there and welcome to the forum.
Wow, it's a long time since I have played with a Socket A mobo and the Beep codes are actually different on this motherboard than what we are used to with today's motherboards.
On this board continuous long beeps would point to a problem with the DRAM and this could be either a faulty DRAM Module or a problem with the socket on the motherboard. If possible check the Memory slots on the motherboard for dust or any corrosion on the contacts.
Check that the CLK_RATIO and CLK_SW are set to auto. If you are not sure how to do this check the User's Manual Page 14 (English version) which you can download from here:
http://www.gigabyte.com/products/product-page.aspx?pid=1756&dl=1#manualCheck the size of the RAM modules are not too large. Page 17 - 19 of the User's Manual give specifications but would indicate that maximum per slot is only 1GB with a maximum of 3GB overall.
Although it can be found in the User's Manual here is a full list of BIOS Beep codes for your motherboard:
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
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
10 beeps CMOS shutdown register read/write error
11 beeps Cache memory bad
