Is there a DVI-I to HDMI cable?

HDMI is a digital-only signal; a DVI-I to HDMI cable is the exact same as a DVI-D to HDMI cable. Your problem would be the result of your video card not outputting the digital portion, or your monitor not accepting the resolution you are trying to use.

Either the video card is not outputting a digital signal (which is likely, if it's using analog VGA instead); or your plasma is not accepting the resolution (many HDTV's will not accept computer resolutions, only HD resolutions). These are issues to troubleshoot with those products' respective manufacturers.