Any question answered...

Confused:
I have used the same computer at work for the past 2 years and now when I plug headphones in to eiother the front or rear headphone jack it continues to play msuic from the onboard speakers while also playing music through the headphones. What's going on?

Your headphones are leaking sound back into the computer. They need bleeding and tensioning.
I've checked the headphone cables and there are no blockages, so there's no possibility of backflow of the sound signal going back in to the computer.

Same headphones? Normally it relies on the plug either pushing some contacts together or bridging them to send a signal to the OS. Either something's broken that mechanism or some kind of OS update or software install has interfered with how that signal is handled.
I tried 3 pairs of headphones. Same problem with each. No change of audio drivers, or OS version (still on XP here) as far as I am aware.