No it should not be glued or anything.
Most likely the plug(s) are on the high side of their max size specifications and the receiving socket(s) may be at the low side of their width specs.
Could be that the plug and socket plastics have stuck themselves together.
Is the computer working or at least in some condition where it can warm up some. If so, allow it to warm up then power down, unplug, and try wiggling the connector loose again.
I do have another idea but it is more risky and requires a steady hand. Have used it in the past - but that was quite a while ago.
Will hold on that idea in hopes that either: 1) Warming up may loosen the plug, or 2) someone else can offer a suggestion or two.