No heat - need help

[itsmywifesX5]

The air inside the car doesn't even get warm, neither the right, left nor rear. Here's my diagnosis:
Coolant is full
Engine temp is normal
The radiator is hot
All 3 hoses going into the firewall don't get hot. The one that comes from (or to?) the radiator is not hot except where it's near the radiator.
The hose going from the engine block to the dual water valve doesn't get hot either
The 2 valve solenoid bodies are burning hot. My forearm accidentally touched it a few times when I tried to touch the hoses at the firewall and nearly got burned.
Once in a while it gets hot for a while just to tease me then it's gone again.

So, please tell me what can be the problem. Bad valve? Blocked heater core? Something else? Thanks.