1995 sidekick starter

I would start with testing your starter a bit more thoroughly. A starter does not always "click" when it goes bad. Often it does nothing at all.
Use regular jumper cable to do this test or a "jumper box." Hook the red to positive and black to negative on the battery when you are ready to do the bench test. Remove the starter and put it into a vice. The "big terminal" on the starter solenoid is where the positive battery cable goes. There are one or two smaller terminals on the solenoid, one going to the "start" position on the ign switch.
On a bench test, the negative battery jumper cable goes to the vice that is holding the starter by the frame. The Positive goes to the "big terminal" on the solenoid. Jump from the big terminal to one of the smaller ones with a jumper wire or a screwdriver blade to actuate the solenoid. It should click and the starter should whirrrrr. If it does, don't get carried away and let it spin freely for a long time - it's not good to run a starter with no load for extended periods of time, especially an old and tired one.
If it doesn't spin, look for another "big" wire going into the starter. On GMs you can usually see it at the other end of the solenoid - it goes into the body of the starter. Carefully touch the positive jumper cable to it and the starter should immediately whirrrr and you should get a good sized spark - that is normal - the starter is a heavy current eater.
If you get no whir from that test then the starter motor is fried inside. You can take it apart and see if it is fixable (new brushes, a clean-up of the commutator and possibly new windings, but at that point I would suggest a rebuilt starter/solenoid assembly.
If the starter did whir on the last test then you can remove the solenoid and either rebuild it or replace it, the later being a good idea. The new starter will come with a new or rebuilt Bendix drive which is probably next in line for failure.

check the positive battery terminal for corrosion, even if you don't see any, clean it off with some corrosion spray or wd40. Take the terminal off the battery when you do this. that should be the first check. Now if that doesn't work, move on to the starter. Tap it once with a hammer while having someone crank the car, if the starter is sticking this will allow it to start. Check the battery first.

There is a fuse on the battery terminal. It seems that this particular fuse has blown. Please replace this fuse.This fuse is like a master switch. Cuts off all electricity circuits.

ok Let me walk you through this,,

1. remove switch from transmission
2. get a piece of wire and connect it to the positive battery terminal..
3. touch each wire on the switch you will see and indicator light up on the dash ,, for example if you touch one,, you will see P light up, ,thats the park wire..,, so you will find wires P,R,N,D,1,2, thats the wire for the shifter..
   
4. connect the last wire on the switch to the wire that light up N (neutral) and you should start..

simple as that..

take the fuses out of the remote starter, if you got the outputs mixed up from the starter you may have fried the starter relay

If the battery is brand new then yes, the starter assembly/starter solenoid (located on top of the starter) is bad.

On top of the starter unplug the solenoid wire. Then make a jumper wire with a spade connector on one end about four feet. plug this into the solenoid and use the other end of the wire to tap the positive side of the batt. this should engage the starter if all is well. if it dosen't, then the problen is the starter.

What about battery charge, check the alternator?

have the crankshaft sensor checked.

my car is a 95 buick century. frequently when i stop and shut the car off , the next few minutes when i try to start it it won't start. i have battery power as far as the whir of the fuel pump, and lights, gauges come on but when i turn the switch it won't start. Is this the starter or ignition switch? After about 30 minutes or so, it will start again.