Yes, you have a 4R70W. As far as not engaging gears, have you checked the fluid level?
As far as a direct replacement I believe you can only go as high as a 98 trans before you have to re-pin the harness to make a 99+ work correctly.
If it were mine, I would find a low mileage takeout from any 99+ Mustang, Explorer, Crown Vic or Grand Marquis and just repin the harness. The newer years had some hardware updates that make them better than the stock 94.
The only issue w/ using a CV trans. is you have to make sure it doesn't have the extended tailshaft used on Police cars. As far as I know the civillian model will work.
Then fill with Mercon V fluid and call it a day. By the way, is your bird a V6 or V8?
These are highly engineered precision vehicles, the first step in diagnosing the problem is to strike the suspected offending part sharply and repeatedly with a blunt object, then re-test.