You have indeed reached the maximum amount that chipset supports.
I have a board using the 945G myself and can confirm that it is limited to ~3.37 GB usable memory, even when you have installed more and all the memory is shown in the BIOS.
For being able to use more memory you might swithch to one of the following chipsets:
Up to 8 GB: 955X, 975X, P965, G965, Q965, P35, G33, G35, Q33, Q35, G41
Up to 16 GB: X38, X48, P43, P45, G41, G43, G45, B43, Q43, Q45
Note that to use more than 4GB DDR2 you want to get a board with 4 DIMM slots, since the biggest RAM modules supportet on intels platform have 2 GB each (which would be either 3x 2 GB, or 2x 2 GB + 2x 1 GB to get 6 GB total, or just going with 4x 2 GB for 8 GB in total)
Of coure it...