major issues with 2001 seat ibiza

[sputnick72]

desperately need help with my 2001 ibiza chill, the engine management light is permanently on and it has a lot of trouble starting, but only when the engine has been run. If i start it from cold it's fine but if i try and start it after popping into a shop and it's only been off for a few minutes i have to wait at least 15 minutes before it'll start again!!
I know i need to get the engine plugged in and read but i was hoping someone might know what sort of issue i have before i get it in to the garage

Any help will be greatly appreciated

Nick