Acura: acura integra 1990, acura integra, battery terminal

Question
my car won't start when the engine cools down, i can only hear the click of the main relay and the solenoid but the starter / engine don't crank, however when connecting the solenoid directly to the positive battery terminal, the starter works... and afterwhich it will start normally until such time that the engine cools down again. i've already replaced the main relay and starter but still it won't start when left for a long time... i'm really puzzled coz the starter works when connected directly to the battery and afterwhich it can be started thru the ignition switch... it seems that power from the battery passing thru the ignition switch is not enough on the first start after the engine cools down...  

Answer
did you replace the starter with the Acura remanufactured ones or from Kragen parts store? Same for the main fuel relay, is the part Acura factory parts or aftermarket?
Is your battery new? If you have a weak battery your starter wont have enough power to crank the engine over.
My guess is your starter contact is worn out inside the starter.