First-line Tech support folks get a screen with a list of articles, possible problems, and a statistical analysis of what problems have been seen in a large number of service visits for this model Mac. It would show that graphics card failure is a common failure, so that might cause them to blurt that out to you as a plausible diagnosis.
Technicians who actually put thier hands on these Macs get a service manual with flowcharts for each of a dozen or more symptoms. The flowchart says, follow theses steps, in this order, and then replace this module. Number one is always observe the CHIME, because nothing else is conclusive until it has passed its internal tests, and that is signalled by the chime.
Check the sizes of your modules. You may have four 1GB modules. If that is the case, you can try all pairings in hopes of getting a pair that works. There are only a few choices.
If you have modules A, B, C, D
A is currectly paired with B and that does not work. so try A + C, and A + D
B is currently paired with A and does not work, so try B + C and B + D
C is currently paired with D and does not work, but you have tried all other combos above.
D is currently paired with C and does not work, but you have tried all other combos above.
Run up to the correct four trials and you will have tried every combination, since A with C is the same as C with A.