Unable to move car forward or backward

How long will the transfer case out of gear be before it becomes a huge issue and I will no longer be able to change gears?

Will I be able to change the cable shifter myself? I'm not the most handy person in the world and I have a limited set of tools, but am willing to get the correct tools if this is something that can cost hundreds.

Once the linkage starts wearing out it will continue to be a problem. It may not necessarily damage the case but it could leave you stranded if you don't know how to get underneath and manually put it into gear and the alignment won't allow it to engage.

The cable shifters run $150-200 and you should most likely be able to do it yourself. There's a lot of write-ups on how to do the install, plus some videos. Not sure what a shop in your area would cost to install, but I have faith that you can do it 👍🏼
 
I had that exact problem and it was my transfer case. It seems that my Transfer case went dry over 25 years, and burnt up. My Jeep just stopped moving. Most people do maintenance on the Transmission and Engine, but not the transfer case. It is the same for the differential. I had my differential serviced just recently. I had to replace my transfer case.