When car is cold run for about 4 to 5 hunderd yards then cut out but stars sright away then fine when warm

Throttle control sensor is where i would start.

run the fault codes as there may be a sensor out of adjustment allowing extra fuel on star but cutting back to far when at operating temperature
could be problem injector controls

What are you asking ?

Sounds like the motor is gone mechanically

Do you have any preventative maintenance done a couple
times a year or any testing done or just wait until it doesn't
run correctly,that is your problem with the car.

You can't start a car & drive away 30 seconds later

It runs off the computer until warmed up & you have very little
fuel control when cold

cheapest thing to try is the temp. sensor about E20 its under the distrubitor 4 wires in one plug then a clip to take out the sensor, if that dont work try to get a lend of a throttle body and change it to see if that works before buying one as they are dear. hope thats some help

I think you know, that the vehicle has to be in the
hands, of a knowledgable technican,so some testing
can be done.

You may spend your first $100, just for diagnostic time

Why would you think anything, if you have to ask?

It sounds as though your warmed up and in closed loop,
before the problem starts.

A long list of possible causes, won't help you,as your not
doing your own work,your paying someone.

change out the engine coolant temp sensor!

Could be water in the fuel causing icing up in throttle system. Try running some heet in the fuel tank.

if u have a damaged plug it can be running on 1 less cylinder ,it will idle very rough,change it!

check the coolant tempetuure sensor .if this does work properly the engine control unit thinks the car is warm when in fact its cold.