Monitor cable often fitted with a pair of screws to anchor it in place and prevent accidental disconnection.
The graphics card and the monitor likely both do not take kindly to plugging in or unplugging while powered up.
At least one pair of pins carries +/-5V while the others carry digital data at micro voltages. If you reach around the back of the box to plug in, cannot see what you're doing, shuffle the plug around until it fits the D socket, you will eventually touch a 5V pin onto one of the data pins and, potentially, cause damage.
7 year old machine, long out of warranty so no harm in opening up the case and checking that the graphics card and motherboard are free of dust. Use anti-static precautions while dislodging dust with brushes and don't use rip-roaring vacuum cleaner power near delicate components.