WEIRD Starter Problem!! HELP ME Please!!!

Okay, guys, I've got a weird problem with my starter. Well, at least I think it's my starter. I've got an 89 celica that has a real hard time starting in the winter time. I know all cars do, but this one's got it bad. If it sits for a long time in the cold and I go out to start it, I turn the key and it just makes a humming sound. No clicking or any attempt to turn over at all. I can hold the key there for 4 or 5 MINUTES and nothing happens!! What I usually do is put the key in the "ON" position and go inside and cook breakfast or watch TV for a bit and then I come back and turn it and it will actually try to turn over.

The weird delay is one problem. The next is that when it does turn over it takes about 3-5 seconds to actually start running where it's supposed to and the engine shakes a lot while it's getting there. It practically hesitates and very slowly and with a lot of shaking it gets to the optimum RPMs. If I push the pedal to the floor it doesn't do anything in getting it running faster, but it sure does put out a ton of white smoke. Please help me with these problems guys!! This is my most dependable car and I want to keep it that way!!