If capacitors are bulging, then those (and maybe some other non-bulging) capacitors are failing or have failed.
Failing or failed capacitors can cause any number of issues, depending on where the capacitors are located and what they do.
The memory controller itself is unlikely to be faulty, the fault is more likely to be "downstream" nearer to the memory slots.
Two options.
1) Replace bulging and possibly other nearby capacitors on the motherboard by a person capable of doing this replacement work.
2) Scrap the motherboard and replace it with another.