94 duster stalling/not starting

I got a 94 Duster with 144k hard miles on it. Live in WI where it is
cold right now, -7 yesterday. Car is kept in a garage, but my daughter
uses it for school, work etc. During the last week she complained
about it not starting. I assumed water in the gas and told her to add
some antiicer which she did not do. Yesterday she calls and said the
car had quit. I got to it, added some heat and attempted to drive it
home. It started right up, but drove about 30 ft. and quit. Sudden
quit, like someone pulled the feed wire off the distributor. Lights
stayed on bright, radio going, everything else stayed on. When I
turned the key nothing happened. Again, lights stayed on bright but
starter did not engage. I tried a couple times and nothing. After a
couple minutes it turned over normally, but did not start. As it was
turning over, it suddenly stopped. Again, turning the key did nothing
for a little while. It seems real random, not just a 'cool down'
period before it turns over. I have it in the garage and plan on
cleaning any/all connections I can find, but don't really know what
else to check. I did not check for engine codes yet, plan on doing
that this morning also. But any ideas where to start would be
appreciated!

Backally Bob