I would start with moving it out of the vicinity of the air vent if possible, at least to try and eliminate it as a source of trouble. Then I would go about unpotting the cactus and checking the roots if you haven't done that recently. The rootball may be compacted with hard peat soil or the roots could be rotten, no telling since you have both squishy and extremely dry parts. My first thought is that it may not be taking up any water.

I don't grow cacti BUT, this is true of succulents in general.

Squishy or mushy = rot & must be removed ASAP, as it can spread & spread quickly. Best to cut the affected area out w/ a sterile blade. Pls be sure to sterilize your blade when done as well. Good luck.

The whole thing looks dead to me. :(

If it's a euphorbia, be very, very, VERY careful of the sap if you cut the plant or even just disposing of it if it is indeed gone.