However, the machine never started after that. It powers on but all I get is a black screen and a buzzing sound from the monitor port. Connecting with the L&R sockets doesn't produce the buzzing.
This problem was almost certainly a Red Herring (a false fault) caused by you plugging the 13-pin monitor plug into the socket upside down. It is very easy to do accidentally and produces the symptoms you describe, especially the buzzing sound from the monitor.
As you kept on faultfinding and removed the plug at some point and put it back in again, this time the right way up, that particular fault went away.
If you have access to some 'Freezer Spray', let the unit warm up until the fault comes on, then carefully spray individual components while the unit is on / fault is present to see if cooling any of them makes the fault go away. Note: NEVER use freezer spray on the PSU unit, use only on low voltage parts of the computer.