I was having the same problem as described above. I have found a solution, although I'm uncertain to the safety of the solution.
In the wp-cache-phase1.php file, find the following line where the headers are rewritten:
What I found is that adding the header Last-Modified causes GoDaddy to have issues. So I added code to ignore the header if it is Last-Modified. If you want to test if this solves your problem, simply comment out the header line and try refreshing (although in the long term ignoring all headers is probably a bad thing). I have a full explanation at my site here.
If anyone could weigh in on my solution and let me know if there is any risk in ignoring the Last-Modified (or any other suggestions), I'd appreciate it.
Also, I'm using WP 2.0.5 (yeah, yeah, I know) and wp-cache 2.1.1.