I'm having a difficult time finding an air conditioning guy to come out. But, in the meantime I've discovered that the smell does not occur when the heat is on. It only occurs when the air conditioner is on. Any ideas about why that is?
Hmmm. Do you mean that you can run the AC all day (and air coming from ducts smells bad), and if you switchover and run the heat immediately afterward the air doesn't smell bad at that immediate time? That would be a mystery, since, no matter where or what is causing the smell, it would still be occurring for at least a few minutes after you changed over to heat (because the air still goes over the A/C evaporator coil, across the pan in the bottom, through the same ducts with any dead critters, etc).
Now, if you mean that a few days or more after the last time AC has been run (and the pan/any mold has had a chance to thoroughly dry out), if you run the heat you don't notice a smell, that would indicate the problem is more likely mold related, highly unlikely to be a dead critter in the ductwork.
Two thoughts:
1) Unless you've got a highly inaccessible installation or you just don't want to mess with it, it's usually not hard to detach the drain pipe and see if a bunch of mucky water drains out. The clog is most frequently in the drain pipe itself, and cutting the PVC near the unit will let the water drain out if the clog is lower than that, and give you a chance to (carefully) push some stiff wire up there and ream it out (if the clog is upstream). Bring a bucket to catch the water/muck, and have a coupling of the proper size and some solvent (aka "PVC cement") to re-join the pipe when you are done. As a backup, have a cap of the right size that you can jam over the end if the drainage is more than you'd bargained for. Also, before you cut anything, see if the air handler has "settled" or been bumped causing the drain point (under the evaporator coil) to >not< be at the lowest part of the internal drip-pan under the evaporator coil. If it's been knocked out of kilter, the drain tube won't be at the low point, water will pool in the internal drip pan and possibly spill into the ductwork, and mold will result >even< if the drain pipe is not clogged. A regular bubble level placed vertically against the sides of the ductwork/air handler will probably tell you what you need to know: is the unit plumb (if so, the drain will be at the lowest point unless it was installed incorrectly or something has come apart inside the air handler).
2) They make UV light "air purifiers" (like
this one) that can be put into your duct/air handler system and will keep any mold at bay if the affected location where it grows is within line of sight of the unit. These are
seldom required if adequate drainage is provided, but it can be a good belt-and-suspenders approach as the units also kill a high percentage of other mold/bacteria/viruses normally in the air as it passes by the light. They are very reliable, but the bulb (less than 40W) needs to be changed annually. If you go this route, be sure to investigate the replacement price of the bulbs and get a unit with inexpensive ones. The "guts" of the bulbs are all very similar (essentially florescent lamp without the regular phosphor coating, so they emit a lot of UV-C light), but some companies use nonstandard ones or make the bases unique so they can charge a high price for the proprietary replacement bulbs.