I'm having the exact same problem with my 96 Explorer.
Everything points to the transmission being rebuilt or replaced. The reverse band broke, came loose etc.
1998 ford explorer transmission reverse won't engage, acts like it is in neutral.
The A4LD transmission is the weakest part of the 91-94 explorer. It is likely that your transmission has failed.
You may need another transmission if your Ford Explorer will not drive in reverse. The best way to find out is to take it to a local mechanic.
Reverse is usually the first to go, followed by first gear. Time for a transmission rebuild.
You need a new gear box (transmission)
clutch plates could be welded to gather
The A4LD transmission is the most common failure on early explorers. It's very likely that your transmission is failing.
check transmission fluid, make sure it is all the way into reverse and make sure the emergency brake is not engaged.
Most likely worn engine mounts or transmission mount.
This could indicate a simple problem with the vacuum shift modulator or a major failure with the transmission. You will probably need to get it to a mechanic or a shop to get it properly diagnosed.
The simple thing to do here is get beneath the transmission and see if the lever arm there is moving to the reverse position - prefereably with the engine not running. It may be a silly milimeter out of adjustment. lol