To begin with it is not required that you convert to r134, which is still by the way called freon. Also it is not true that the r12 supply in the future is uncertain. There is plenty of R12 and there is less demand for the stuff with every passing day. This is because the cars requiring it are at least ten years old now and starting to hit the wrecking yard.
Although they no longer produce it, there is an ample supply on the shelf plus much of it that is being recovered and recycled.
The second myth to be disspelled as far as the 124 a/c goes is that if there's something wrong it must be the evaporator. This is not true, it is very possible that there is a leak of another type or location.
Myth number three is that 134 works okay in a 124 car. This is true to some extent because it will indeed make the system blow cold air. It does, however, cause the system to lose capacity and the 124 a/c is marginal in capacity even with R12.
Now that we've cut through some of the myths that are floating around, let's start troubleshooting your car. The first thing you should do is start it up and turn on the a/c with the middle button and the top fan button. Give it two or three minutes at about 1500 RPM and then look at the sight glass located on the filter drier just behind the drivers side headlight. Are there bubbles running through it. If there are not, look at the a/c compressor clutch on the front, bottom of the engine near the filter drier to ensure that everything is turning. If everything is turning and the sight glass is clear then your system has adequate refrigerant.
If the a/c clutch is turning and there are bubbles flowing through the sight glass, then the system is low on refrigerant. In this case, you need to find the leak, fix the leak and recharge with R12. Another myth that has yet been mentioned in this thread is that R12 is $100 per can. It can be had for $29 per can, but only by someone with 609 certification.
The other scenario is that the a/c clutch will not kick in. In this case you are probably low on refrigerant. There is a pressure switch that prevents the clutch from kicking in under these conditions to save the compressor from damage.
So, do the sightglass test, post the results and we'll take it from there.