Some random thoughts:
I always forget that my local firewall can block outbound traffic. I think I hit this same issue with nmap. Try disabling your local firewall or creating a policy that allows all traffic out which originates from localhost.
If that isn't it then forget nmap and focus solely on getting ping to work. If ping currently doesn't work then this will help you find the point of failure.
The ports on the server might be open, but are they exposed to your source IP or network segment? They might be open only for localhost. Disable the firewall on the server for a minute to see if that helps you find where the blocking is occurring.
You said the ports on the server were open. I'm assuming you have tested this. Try a netstat -an on the server just to be certain that it's actually listening on those ports.
Is there any potential for blocking inbetween the devices? Does your traffic traverse a router, other firewall, etc?
One other random potential issue: Sometimes my apps just don't work on Win7x64 unless they're running as Admin. Even if I launch them under an account that has admin privs, I still occasionally have to right click on them and run them as administrator. Perhaps...
As @Ryan said; map out the potential choke points for your traffic and starting testing each one.