The distributor going out in the Galant is pretty common, and usually needs to be replaced at around 100,000 miles. Along with the distributor, you should replace the spark plugs and spark plug wires. The wires can wear over time and should be replaced around the same time the distributor gets replaced. The spark plugs should be replaced per the owner's manual suggestion; usually every 30,000 miles or so. Your plugs may be worn out and no longer can produce a spark. They could have either burnt out or are not gapped properly.

Another problem to look for is oil or excessive moisture could be leaking into you spark plug wells. This can be easily checked by looking around your spark plug wire boots to see if they're torn or just plain worn out.

For more of the broader picture, make sure your battery is charged properly. If you have a voltmeter, you should get a reading of 12 volts across the battery terminals when the car is turned off; and between 13-14 volts when the car is running (that'll let you know your alternator is working). If you don't have these tools or don't feel confident checking, any qualified mechanic can check for you. If you have a mechanic check it out, also have him/her check every voltage reading from the battery to the ignition coil. There may be a short in the system preventing a spark from firing.

There are many things that could lead to a spark plug not firing, but hopefully the suggestions I provided will help trace the problem to correct area.

Good Luck!
Anthony