it's been done before by about 95% of the users of this forum.
I'd say that very few people use head units with their installs...I know I haven't in over 3 years.
You need to spend some time searching.
The CD player is a non-issue. There are adapters for laptop CD-drives out there.
The Radio question has been asked about 10,000 times on these forums. I suggest you search on that one especially since it's not a cut and dry answer that I think you're looking for. You need to understand the ups and downs of each option out there before you make a move on that one.
Regarding the sound card....there's an entire stickey in the car audio forum that discusses avaliable USB/FireWire sound cards. There's also a lot of talk in there about higher end PCI sound cards.
There's a TON of information on this forum. It might be overwhelming at first, but it's imperitative that you use it to your advantage if you're going to be taking on a project like this.
Getting your car to sound great while using ONLY a CarPC is very possible. Just check my signature to see what I mean.
There are a number of us on here who compete in SQ comps with computers. Some with HUs some without.
Though, this hobby isn't quite as easy as picking up a radio off of the shelf and just splicing it into the wiring harness.
There's a lot more that goes into it if you want to play on that level.