No a/c or heat

The climate control system on my 2001 Jimmy blows the same temperature air no matter what setting I Have the controls on. I CAN hear the difference in sound as to where the air is coming from when I switch it from from hot to cold so I do not believe it is the blend door gone faulty.

The problem started when one day I turned the air conditioning on and go not air at all from the vents (hot or cold) i would let the truck sit for a couple minutes or just drive it with the controls off and it would eventually work until one day it decided not to blow out cold air (that was last summer), then last winter went to use the heat for the first time for the season and realized that I had no heat. I have been just dealing with the problem since them but am anxious to get both my a/c & heat fixed any suggestions?

What I have did:

Back flushed the cooling system in efforts to flush out the heater core
Checked the fuses for climate control inside the cab (ok)
Checked connections at back of climate control knobs in dash (all tight)
The a/c compressor does kick on when running the defrost I know this for sure.

Should I check the or have checked the level of r134a in the system?

For the heat, it may be a clogged heater core...Descool sludges up and clogs it... Do a reverse flush on your heater core and see if that cures it. For the AC have you checked freon pressure?