I think cleaning the vents is an easy fix, but honestly at this point, you'll probably appreciate having a new console more? Not only will you have PS4 BC but also access to the new games. If it were me, I'd go for it at least.
I cleaned all the dust out and it lasted for 6 to 7 hours put it on sleep mode and a little later it was off.
The fans not loud at all but when I turned it on I had to move the HDMI cable a little then it came on.
So if it losses hdmi connection will the ps4 cut off.