First a few details. What year is this? Engine? Transmission?
When it doesnt turn over do you mean it wont start or that the starter truly doesnt move the engine?
If it doesnt move, do your lights dim when you turn the key? If not I'd guess the relay's gone out. If so, bad wiring, low battery or failing starter.
If it Does move, do you hear your fuel pump run for a moment when you turn the key on? Might not be getting any fuel until it's been cranking long enough for the oil sensor to kick it on.
Does the shifter move nice and free when the car is not running and stationary? If it shifts just fine then you might be looking at clutch related trouble. Otherwise I'd suspect something a little deeper. Also does it get better once it's warmed up? Might check your fluid level and condition.
On my '84 manual I discovered the slave cylinder had actually come part way unbolted, making for some interesting clutch behavior. Didnt notice until someone else pushed the clutch in with me watching the slave. Whole thing rocked front to back.
Also dont forget that there's a way to adjust your linkage, and if it's not right you will have a heck of a time shifting. It's quick and easy so you might try it.
If your car has a shared temp/oil light it could be eather one setting it off. My oil sensor became rather gummed up and would trigger the light. Stayed that way until I hit it with a hammer. On the Duke you can reach down under your intake, to the right of the distributer and unplug the oil sensor. If your light no longer comes on like this, the oil sensor is to blame. If it keeps going it's time to check for pinched wiring or a temp sensor going wonky. Dont forget that air in the coolent can even cause the temp sensors to act funny at times.
And above all else, remember that I am new to the Fieros and shouldnt be considered a know-all source!