Yes, sounds like a bad ignition switch, not a back lock cylinder. I replaced the switch on my 88 XJ 18 months ago. You need to find a friend who done a GM ignition switch before to be there for moral support. Also go to sears and pick up a set of Metric "igniition wrenches" they run less than $15 for a set, they are very short wrenches which allow you to get to the bolts. The ignition switch runs 10 to 15 bucks, I stalled a borg-warner, I'd also feel good with an AC/Delco... for the price I'd go with only those brands.
You will have to remove the dimmer switch to change the ignition switch, then reinstall both. It up to you if you want to change the dimmer switch, but 2 weeks after I changed my ignition switch the head light switch went out. I changed it and in the past month I changed it again with a head light switch from the dealer. You will have the dash apart, not much more effort to change the head light switch. I paid $35 for the dealer head light switch, I'll pay that for a switch that lasts 15 years...