The models I looked at few HP G60-xxxxx all listed 2GB/slot max so even with a 64-bit OS upgrade won't help. Addressing 2^32 = 4,294,967,295 bits limit ~4GB and change.
OS RAM support -> http://msdn.microsoft.com/en-us/library/aa366778(v=vs.85).aspx
Memory Type: DDR2 PC2-6400, DDR2 (non-ECC)
Maximum Memory: 4GB
Each memory slot can hold DDR2 PC2-6400 with a maximum of 2GB per slot.*