Why does a 1998 Corolla sometimes make a loud 'click' sound instead of turning over engine when turning key to start?

Answer 1

Free - take you vehicle to a store that will "Load" test you battery for free. They should remove the wires from the terminal during the test, clean them, test, and if the battery passes... reinstall them. They may try to sell you some felt red and green discs, though. They should only be a few bucks and are probably worth it (the discs are saturated with a chemical designed to reduce corrosion.
Problem with the above... if your battery fails the load test, you need a new battery. Based the 'warranty' of the battery on how long you'll keep the vehicle - buy cheap if you sell in two years... buy expensive if you're keeping it for life.

Almost free - remove the battery terminals and clean them yourself. Be sure to wear safety glasses or equivalent. If you don't have to brush/scraper 'battery terminal cleaner tool, then go buy one. If the bolt on the terminal clamp is shot, it is BEST to replace the whole wire (ranging from a few inches in length to several feet depending on vehicle.

Problem with the above - you are only cleaning the terminals and not load testing the battery. But, it seems that when the weather turns in the fall, the fix is just cleaning terminals.

Nearly every tire store or Wal-Mart will do this test for free. probably even Sears. If you're charged, move on to a free one.

Almost worst case (but could be free) - starter electrical contacts are worn. If the terminals are clean and the battery is in good working order, then this is the case. If you have mechanical skills, pull the starter. If it is a traditional older style starter, (carefully) bust into the (smaller) 'can' where the fat wires connect and rotate the worn copper bolt head 180 degrees (one will likely have half of the bolt head worn down). Carefully reassemble and install. If there is no worn head, then abort and buy a new starter.

Worst case - buy a new starter and install it.