For someone with lots of graphic design experience but not a lot of computer experience what would you recommend: Photoshop or corel. I am sure they can be used together and each one is better for certain projects. But I only want to learn one at a time.

It depends more on your preference since some people likes photoshop while others are inclined to corel draw. Just learn the one that you think is better and you could forget about the other since you could just do the same thing with each program.

I've used both but since I'm more into coding web layouts rather than drawing, I preferred Photoshop. Another advantage of PS is the amount of documentation available, there are tons of books and free tutorials out there on the web to learn it. Get the free trial for each though and see which might suit you best.