Toyota Repair: 92 Toyota Corolla, toyota corolla, battery connection

Question
We have a 92 corolla with only 34,500 miles on it and within the past year or so have replaced both the alternator and battery.  Had to have it towed yesterday because it died while driving. Lights went dim then it died.  After it sat for about 1/2 hr we tried to turn it over and it started.  Drove about 2 miles and it did the same thing again, lights dimmed then it died.  Instead of chancing it on the freeway to get it home we called for a tow truck.  While waiting on the tow we kept the car running with the lights on for an hour and it never died.  What could cause the lights to dim then the car die only when you are driving it. Once home, we turned it over again and it started right away, no problem. Any suggestions on what to check next?

Totally Confused

Answer
Find a test light or volt meter.
Touch the two posts of the battery and see what the voltage is or how bright the test light is.
Then touch them at the terminals, and compair.
If there is a differnce in brightness, or voltage, you have a bad battery connection.

Get some battery cleaner and check to make sure there tight and clean.
Check the wires at the Alt plug. the get brittle from heat. tug on them, see if they break. Then repair as necc.

Mike