My Saturn starts sometimes and sometimes does not....I it not the battery, and a brand new starter was put in last year...sometimes it will start a couple of times in a row and then wont start...I am still getting power like the lights, radio, door alarm, etc.... I am stumped. It usually starts when it is cold. But most of the time you can start it once then turn it off and then wont start.

It's possibly the ignition switch or the battery cable going to the starter . Would need to do some testing to say for sure . Can you do electrical testing ? Have someone turn the key to the start position and someone check for B+ voltage at the S terminal on the starter solenoid . If B+ voltage is there , voltage drop test the starter circuit . How to voltage drop test starter motor circuit Starter Voltage Drop

Park neutral safety switch maybe be the reason for the no crank ! Try putting the vehicle in park ,then try to crank the engine . Testing the electrical circuit is the best way to trouble shoot this problem , along with do a voltage drop test on the starter circuit ! This will test the battery cables an connections .
Starter Voltage Drop
How to voltage drop test starter motor circuit
Does it have a manual or automatic transmission ? Manual ? clutch switch . Looking at a wiring diagram I also see a starter cut relay !
http://www.bbbind.com/free_tsb.html Free wiring diagrams . Enter vehicle info. year , make , model and engine size . Under system click engine , under subsystem click starting . Then click the search button , then click the blue link ! Check the starter cut relay also . Videos on youtube showing how to test a relay controlled circuit !

Recently we had to put a new fuse in the starter ???????????? What fuse ? location , size . A fuse blowing means a electrical short to ground .

doubt it, maybe check ignition relay or starter solenoid

it might not be the starter it could just be a relay i would check the relay and if it is just clicking when you try to start it then that is probubly it if not maybe you have a bad batery

Single click? More battery is needed. Id change the battery, or slow charge it.
Might also be the security system shutting down the starter. Common on GM vehicles. Heres a link on that. http://vatspasslockpasskeysecurityhelp.yolasite.com/

I was having the same problem with my 2004 9-3. I assumed the starter was bad and replaced it. I then charged the battery and found it wouldn't fully charge. After charging for several hours when I removed the charger I only showed 11 volts at battery posts. The new battery tested 12.8 volts and the car started well. With the car idling I tested and showed 14.6 volts at the battery post which confirmed my alternator was charging.

I do believe I replaced the starter in error and that it was just a bad battery. When my battery was failing I had dim headlights and flashing displays that you described and the clicking noises also. When I put jumper cables on my saab and let the bad battery charge for several minutes the car would start right up and the headlights would brighten up and even though the battery was bad the idle voltage at the battery posts was increased to 14.6 volts coming from the alternator.

Remember to remove the jumper cables quickly once the car starts to avoid possible electrical problems.

I have had bad starters in other vehicles that would draw a huge load on the battery and jump starting them would sometimes give enough voltage to turn the engine over and start it.

Bench tests aren't always correct because the components aren't under a true load. I had a brand new alternator fresh out of the box last year that was bad and wouldn't put out good voltage even though it bench tested perfect. Go figure.

Check your battery voltage with the engine off. It should read over 12 volts if its charged.

this is caused by burnt starter solenoid contacts, U can either replace the starter solenoid contacts (about $15) or u can replace the entire starter.

if you have good battery voltage at this time, and when you banged on the starter and then the car cranked over, it would appear you have a defective starter. i would imagine if you replaced it in july of last year that it could still be under some sort of warranty, so i would look into that. either way, it sounds as if you need a new starter.

Have you changed out the starter, sure sounds like a starter or starter wiring issue.