I bought my '68 390 'vert in Dec. It has factory A/C that worked when I bought it. All of the heat, vent, A/C stuff worked correctly with the exception of the "heater core bypass thingy" which had been bypassed by PO. I re-connected the hoses to the bypass just to see what would happen. At the same time, I replaced the fuse to the clock and got the clock working. HERE's the problem: Now whenever I turn the fan on any speed, the A/C comes on and blows air out of the floorboard vents where heat normally comes out. Sliding the other switches (temp and selector) has no effect (that is, A/C is always on and always blowing out of the bottom). I can't get any heat. I disconnected the "heater core bypass thingy" just as PO had done, but that did not fix the problem. I can't believe the clock has anything to do with this, but it is the only other thing I had done at the time.
Sounds like you've got vacuum problems. The "Selector" switch is just a vaccum router. It directs vacuum to various "motors" that open and close the vents. There is also a switch for the AC in line with one vaccum hose.
It sounds like you're not getting any vaccum to anything. All the stuff under the dash runs off one hose that goes to a reserve can (looks like a black old coffee can) under the right fender. One hose gets vaccum from the rear of the engine intake and goes to the can which should have a check valve that holds a little vaccum after the engine is shut off. I'd start at the intake looking for damaged hoses and go from there. If the heater bypass is disconnected, make sure the vaccum line to it is blocked off too. It should have no effect on the rest of the vents as long as it is blocked off.
If you have to get under the dash, you should buy the Osborne Vacuum diagrams. It starts to get complicated under there. I used a hand vaccum pump to test my set up. The vents should bang and clump a bit when opening and closing. You should have just enough vacuum in the reserve after shutting off the engine to make at least one "clump".
Hope this gives you some ideas.
There should be a micro switch on the heater control panel that operates the compressor when ac mode is selected. Make sure it is not sticking. I am not sure about 68 but that is what Ford did in their later years. As far as the heater hose bypass valve is concerned the po probably bypassed it due to a leak or because it wasn't functioning properly, To some people it is cheaper to cut it out then replace it...