I'm no expert but I had a unit that was dripping into the bottom of the air handler. If your heat exchanger coil is dirty, some of the condensate may build up and drop from the center of the coil instead of running down the fins into the collection tray. I would start by cleaning the coils with the appropriate cleaner. Of course at 17 years and 84 degrees, you are burning money with that old unit. BUT, after I cleaned the coils things worked a lot better.
My first house had ice building up on the coils..turns out the previous owner NEVER installed a filter and the entire coil assembly was covered with dog hair 1/4 inch thick.

you could have several things causing this. most likely is a plugged up drain pan. also, gunk buildup on the coil or inside the drainpan itself can cause this. also you could have some insulation missing or damaged somewhere in the supply line causing moisture to accumulate on the outside running down the cabinet and collecting at the bottom of the unit. investigation is the only way to know where it originates.

Thanks for the good suggestions. Again though, it's inside a closet with almost no access. The front has a piece of dry wall nailed into the 2X4 supports that hold the unit above the ground. It has 3 cutouts where a copper tube, the pvc drain pipe, and a larger insulated pipe come out from. I could cut the dry wall and remove 2/3rds of it to look inside. The only other access is through the opening where the air filter is installed.
For what its worth, I can see the coils from the air filter access...and they look very clean. The A/C unit has never been run without a filter. The water seems to be dripping down from the middle area...so I might be able to put a bucket under there for now.
I intend to replace the unit - but I was hoping to buy some time. In another month or so the A/C will not run much at all due to somewhat cooler weather, and I'm told you can find better deals for A/C installs when the demand is lower.
Flessan