First thing I'd do is remove the CPU, check the pin area on both the mobo and CPU for dust, burn marks, etc. Then reseat the CPU and heatsink.
moved the RAM around in the slots
"Moving RAM around" will rarely fix a memory problem, you need to eliminate the variables. If the system wont boot (aka you cant test the RAM), you should remove all but one stick, then replace that stick with another, then do the same in a different ram slot. Only one stick of RAM in the mobo at a time.
Main: i5-3570K, ASRock Z77 Pro4-M, MSI RX480 8G, 500GB Crucial BX100, 2 TB Samsung EcoGreen F4, 16GB 1600MHz G.Skill @1.25V, EVGA 550-G2, Silverstone PS07B
HTPC: A8-5600K, MSI FM2-A75IA-E53, 4TB Seagate SSHD, 8GB 1866MHz G.Skill, Crosley D-25 Case Mod