Yes, the HD 6850 supports that resolution and higher.
Depending on how much you want to do before you RMA the computer system, you may want to try to do a fresh install of Windows using the HD 6850. Boot to the Windows installation disk (if you received one). See if the card comes to life with the installation program's generic driver.
If fact, you could use any bootable CD/DVD to see if the card is working. If it works when booting from the optical drive, then you would know it is a Windows related problem. If it doesn't, it almost certainly indicates it is hardware related.