Listen to the beeps carefully again. The number of beeps indicate the problem:
1 = DRAM refresh not working
2 = Parity circuit not working or parity status bits are not cleared when parity is disabled
3 = First 64k memory test failure
4 = System timer is not counting properly
5 = Processor register tag test failure
6 = 8042 keyboard controller Gate A20 error
7 = Processor exception error encountered
8 = Display memory R/W test error (non fatal)
9 = ROM BIOS checksum error
10 = CMOS shutdown register Read/WRITE error
with the code and the fault you can now proceed to a more precise search. If it is the 3....that sounds unfortunately like motherboard, or even like the processor internal cache....