Re: Two general GM questions from a former Jeeper.
On a 2wd converted 203 your shift pattern should be this (starting at the dash side and ending at the seat): 4Lo-2Lo-N-2Hi-4Hi. Locking the hubs before engaging the 4wd from the cab seems to lock the gears in better, but will probably depend on your truck. Truck will probably have to be rolling a bit to engage from 2Hi to 4Hi, for Hi to Lo you'll need to be in Neutral (on the transmission) to get it all the way forward and same for Lo to Hi. On the transfer case itself the outside (frameside) lever IS the Hi-Lo lever, it's pattern being, from front to back, Hi-N-Lo. The inside lever is 2wd-4wd, it's shift pattern being, from front to back, 4wd-2wd (I don't remember if there's a Neutral in there, but if there is it's in the middle).
Your problem could be any one of three things. 1) your shifter's shot; this is common problem with the 203, it's hard to find a replacement, I was lucky to find one from a transmission mechanic's former workplace in arkansas. There is a twin stick available from Offroaddesign.com, it's $170. It's a really neat setup; one shifter for Hi-N-Lo, the other for 2wd-4wd. 2) You're linkage is mis-adjusted (the easiest and cheapest). Get a haynes or chilton's manual and follow the instructions for adjustment. It's really simple. The instructions call for alignment with a drill bit in three adjacent adjustment holes, but the gist of it is getting each lever to fully pull the linkage. 3) jammed or broken fork in the t-case. This is some work and the case probably will need to be pulled. A rebuild kit is about $300, not including the chain (another $120, if needed).
Before jumping to any conclusions or spending any money I would first disconnect the linkage and manually engage the levers using a pry bar. Check to see if your 4wd is working with the hubs in the FREE postion so you can actually see the driveshaft turning under it's own power (rather than from the turning wheels). If you have a body lift it's easy to see from inside the cab with the shift boot removed.
I hope this helps. I went through this whole evolution recently so it's fresh. If you have any other questions feel free to ask.