1986 toyota corolla, rough idle, dies at stop lights then wont turn over .

I own a 1986 toyota corrola carberated 4 dr. Lately my car has been dying on me sometimes when idling or coming to a stop. It always starts when cold but when it dies on me it will not turn over for 3-5 minutes. Also it seems to hesitate when i give it gas while driving especially when up hills. I took off the fuel filter and blew through it and it seems to have only a little resistance. The car sat for 6 months with 1/8th of a tank of gas in it and i have now been driving it for about 1.5months. I tried water remover a few weeks ago and have just changed the air filter. I also just added a complete fuel system cleaner. What could be causing it to die at low speeds or at a stop light and then not turn over. It starts right up when it does turn over. Battery Levels seem fine. I am lost as to what to do next.