SlingPlayer- whether you install the stand-alone full app or the Web Player plugin- shouldn't do anything in the slightest that would cause Windows to utterly fail like what you're describing. I have no doubt it is a frustrating coincidence, but there has got to be something else going on.
The worst I've seen or heard is that the Player app won't launch. But totally borking the OS and leaving the computer in a non-bootable state ? Very unlikely.
Troubleshooting Windows with the problems you're describing is over my head, hopefully someone else will chime in who knows more about that stuff.
If there's any way you can run a guest OS off the optical drive that won't modify your hard drive contents, you can at least see if the hardware will start up and hopefully back up some files. An Ubuntu Live CD maybe ?
I wish I could offer a better answer, but I think you've got bigger issues than the SlingPlayer.