Hard start, cuts out when I take corners after being driven a while

Okay, so the car has a major problem. It has a small hole in the transmission. But it has ran okay up until now. I know that is a degrading problem, but I just need it to run long enough for me to replace it. Right now it is having an issue where if I take it on an hour drive it can only stop maybe one or two times before it has trouble starting. It does not do to bad under thirty miles distance. But now that it is cold out it does not want to start. I can hear the motor turn over but it does not want to fire. It also seemed to cut out when I take corners after I have driven a while before this happened. Is there anything I can do? And how much will it coast me to keep it going?