No AC and Vent blowing hot air

2003 Jetta-my daughter's car. AC stopped working and even with the AC turned off and the temp set to the coolest setting its blowing HOT air. AC button still lights up when you turn it on. Didn't notice any fuses blown, but not sure which fuses would be involved? Anyway-there are lots of AC threads to try and sort thru-not sure if this is one related issue or two separate issues-that just happened at roughly the same time?

See this thread: Cabin heat out of control

Does the compressor engage, and do the coolling fans come on when the AC button is pushed?