What kind of TIM (thermal interface materials)? Most, but not all, are nonconductive. If nonconductive, this should not cause any electrical risks but certainly can degrade electrical continuity through a contaminated contact point. If metal based TIM, then the risk of permanent damage is possible.
A contaminated socket may result in system crashes but that would
not cause the monitor to buzz. Where exactly is the buzz coming from? From inside the monitor case, or from the monitor's speakers (if it has speakers)? If from inside the monitor case, that's a monitor problem. If from the monitor's speaker, it probably is the computer, itself.
When you were doing maintenance, did you take the necessary ESD prevention procedures? That is, did you unplug the computer from the wall and touch bare metal of the case interior BEFORE reaching in, and frequently thereafter?
Triple check to make sure while you were digging around in there you didn't knock any cable loose.
^^^This^^^
I recommend using
CRC QD Electronic Cleaner or
WD-40 Electrical Contact Cleaner. Typically, the power from the spray is enough for most cleaning jobs. But if the dirt is stubborn, I spray it with the contact cleaner then give it a soft scrub with a
acid brush. Then spray it again to let the dirt and grime drip away.
I prefer and recommend using acid brushes as they use "natural" boar hair bristles, specifically chosen as they are non-interactive (won't melt or dissolve) with most solvents. While contact cleaner is [supposedly] safe for most plastics, I personally would not risk the possibility of having plastic bristles of a toothbrush dissolve and get in my CPU sockets

. But that's me. Plus, $6 for 36 acid brushes that you can use for all sorts of tasks is cheap!
I would orient the case (or removed motherboard) so the socket is facing the (newspaper covered) floor so excess contact cleaner will drip away - instead of puddling up on the board. Clearly, eye protection while spraying UP into the CPU socket is advised. Note excess contact cleaner will NOT hurt the motherboard or surrounding devices, but it may discolor (or take the shine off) surfaces if exposed to the cleaner for extended periods.