A couple things that have happened to me on my '92 T/S - check your key.  If
you have a resistor pellet in your ignition key the contacts may be dirty
(like pocket lint).  Or they may have worn to the point where they don't
properly make contact in the switch all the time.  A new key (not cheap)
fixed my similar problem for many years, then it happened again.  Only this
time is was a broken wire to the switch, preventing the security system to
see the proper value to enable the starting system.  The break was within an
inch of the switch.

If this happens to you again check the dash and see if you find a security
light on - if so, you can wait 3-5 minutes and try again.  Several attempts
increase the waiting time, which may explain why you still had a starting
problem after cleaning the battery connections.

My T/S has 195K+ miles, going strong...