Sounds like your transmission solenoids are toast or very dirty/corroded.
I have a 95 Cherokee also, and after some mudding and water crossings, I too had the same issue as you. I shifted from Park to 1st repetitively with the Jeep on, and also several times with the Jeep off key half forward and I drove off without a problem. Your probably need cleaned or replaced. If that sounds like a "p i t a" go ahead and find an AW-4 from a scrap yard and swap them. The AW4 is a high mileage durable transmission and very cheap.
I have a 95 Cherokee also, and after some mudding and water crossings, I too had the same issue as you. I shifted from Park to 1st repetitively with the Jeep on, and also several times with the Jeep off key half forward and I drove off without a problem. Your probably need cleaned or replaced. If that sounds like a "p i t a" go ahead and find an AW-4 from a scrap yard and swap them. The AW4 is a high mileage durable transmission and very cheap.