There are a lot of online storage solutions that will allow you to do that, Internetwhizzkid. But because of the storage capacity required and the potential bandwidth you'll be using, they wont be cheap. I'm sure that you've found that out already.
Another possible, relatively inexpensive, option, is to set your PC up as a private server, using RealVNC. click here The free version wont do what you want but one of the paid for versions, which allows file transfer, should. You could download the free version to try it out, it works well for what it allows you to do. I haven't tried the paid for version as I haven't needed it.