Evaporator coils cold at the bottom and warm at the top

I just bought an almost 100 year old house which hasn't been well maintained. Unless you consider "maintained" to mean "everything done by a handyman who obviously either didn't know what they were doing or didn't have the right tools."

Right before I bought the place, the AC compressor was replaced because most of the fins were practically disintegrated. It seemed to be working well enough that I didn't really investigate past "it works." After I moved in, the place would not cool down. I had someone come out and do a full service on the AC system. Flush the system, refill freon, etc. I actually cleaned the evaporator coils myself before they came (at their suggestion) because they thought there was a good chance that was the issue. It turns out that when the FHA inspector required "replace AC unit", that's exactly what they did...and all they did. Took out the old unit, hooked up the new unit.

Now it's about two months later, and after finding out that my heat didn't actually work right**, my AC is now back to not cooling the house again.

I've been digging around a little, but I took a non-contact IR thermometer to the evaporator coils while the AC was running, and the bottom of the coils are in the 30 degree range and the top of it is around 74 degrees.

If you had to guess, what would be the culprit? Based on what I'm seeing, it sounds like it could be low freon...which means I might have a leak somewhere. I don't think the coils have frozen over, but there has been water on the floor by the furnace. However, I just realized the whole evap coil and drain pan isn't supported correctly on the back side (shocker!) and is tilted away from the drain side. It could just be overflowing from running for hours and getting a ton of condensation dripping into it.

I'm sure I'm going to have to call in a pro to fix this correctly, but I'm trying to learn about the things that might go wrong in this house, and would like to be able to communicate as much info to a service tech as I can. I've been working in people's houses for the past 20+ years and it's SO much easier when someone can actually describe a problem to you correctly, and has made a concerted effort to troubleshoot the issue for themselves. Even if they're wrong about what they think it is, the more info the better.

Any info would be appreciated!
Thx


** I found out the HVAC control board on the furnace was bad, and there just happened to be a new control board sitting in the mech room right next to it. Hmm...suspicious. I go to put it in and it turns out it's a universal replacement because the original one is discontinued. Fast forward to me actually getting all the correct parts and conversion kit. Loooong story short, but the first and last burners weren't lighting... I found small screws INSIDE the gas jets on the first and last burners. They had been screwed in to block the openings. Sigh.

I work in the gas service field and inspect furnaces for safety and never seen screws in the orifices?? To me that sounds like somebody did that and didn't come that way? Do you have a picture of it and where the screws were? Orifices can get blocked if ignored and if burners aren't lighting, flash ports could be blocked. Sometimes can be cleared with a simple blow hose or dental picks. I'm not an AC guy but had a similar issue with my wife's AC unit at our preschool, the coils were covered in caked on lint and dust over the years and never cleaned. Filters only do so much, clean coils get your flow back or at least better.��