First things first, you cannot be "Cheap" with these cars. Invest in the dipstick?

I'm assuming you have a 722.6 transmission? Can you confirm?

If it is stuck in third, it can be broken spring in the valve body-Easy fix...

Now, since their is no history on fluid/filter changes. I figure your fluid has changed from a fluid with lubricating and hydraulic properties to a fluid that resembles greasy pea soup. I figure all you need to do is a whole fluid exchange to get all of it from cooler lines, valve body, cooler, torque converter, etc.. The fluid and filter replacement needs to be recent.

Before any transmission diagnostics can be done. The fluid and filter must be no more than two years old, and the fluid must be at a proper level.

Old battery may give you issues if the voltage is low...

Measure the battery while running, and it should be over 13v. Once the car has been off for several hours. The battery should not drop below 12v.

Best of luck,

Martin