Ok, having a couple problems with my 1993 Mitsubishi Diamante so Im gonna list all the problems to see if they have to do anything with my main problem.

1st thing i noticed is the car will not stay cranked with the AC not on, and when it cranks with the AC on I have to rev the engine a few times before something cuts on in the engine(I hear something turn on then the car stays on)-------this all started after I took my battery out to gain access to my headlights.

2nd thing I noticed is when driving on the highway(with foot on the gas) and I turn the AC off, the check engine light sometimes goes on and then off.

3rd thing I noticed is that my spedometer kinda wiggles and moves even when I have cruise control set. for example. if im set at 70mph, the neddle toggles between 70 & 80mph

The other night I broke my keyy off inside of the driver side door, luckily had a spare key.
next day I went to start the car and no start just a loud click, waited a few hours and the wah-lah the car cranked. Drove back & forth to work a few days and then the car shut off all of a sudden while coming to a stop sign, attempted to start the car and no start again just a click. Next day tapped on the starter and wah-lah instant crank.
Replaced the started and still no start just a loud clicking noise and lights dim really low when I attempt to start tthe car??????????

I had the batt and alt. checked before I replaced the starter and they were fine.

So what Am I missing?
Ive heard check wiring, theft deterrant system, starter relay, main relay, Batt, grounds etc.

How do I go about checking these things or could it be something diff?

you check the battary cable itself
the one that runs from the terminal to the starter

use solid metal battery clamps on both battery terminals

then check the earth strap to the body or motor make sure it is ok

what is the earth strap?

about to check the cable now, is the anything specific i need to look for?

what is the earth strap?
the battery cable off the negative terminal

corrosion /broken wires at the connector or at the starter motor end

I checked the neg cable, changed both neg and positive terminals, checked batt connection at starter and no luck.

dose the starter have to be grounded? cause I noticed that it is not

the starter is grounded by being bolted to the motor

is the starter a s/hand or a reco

next to check is the engine computer unit
or an imobiliser fault if fitted

Sounds like voltage drop to the starter motor - it doesn't get enough volts to actually start.

You could get a sparky to install a relay.

Make sure your battery is topped up with distilled water and the correct size for your car - it might be too small.

The alternator should be charging the battery at between 13 and 16 volts when its running - any less and your alternator needs replacement.

Sounds a bit like one or more of the checks that were made didn't spot something.

Two things you always want to remember with starter motors is the solenoid connection and any earth connection. Leave either off (one is just an electrical plug and the other is usually a bolted down wire) and the starter will do nothing as you've noticed.

I guess you could also have oil and grease contamination in the starter somewhere, which would explain the intermittency of the problem and why tapping the starter allowed you to start immediately from a not-even-cranking position. Try degreasing the starter if you can remove it and notice oily deposits anywhere. If they contact its bushes, they will stop the current flow needed.

This is a bit of a long shot but one of the problems with any kind of connection, earth wire or small electrical plug, is looseness, resulting in a weak metal-to-metal contact. I know that starter motors are notorious for this. You might need a thicker washer or to fit a new electrical plug to fix that kind of problem. Basically if the connections aren't firm, you get intermittent performance (sometimes works, sometimes doesn't).