If your TV "has the DVI input", HDMI is irrelevant.
If your TV has an HDMI input, different story, different answer.
HDMI (high definition
multimedia interface) is video and audio.
DVI (digital
video interface) is video only.
Two different standards.
HDMI is based on DVI and is backwards compatible - i.e. you can carry video-only out from a DVI-enabled component to an HDMI-enabled component. You won't get the audio.
http://www.siimage.com/documents/DVI_HDMI70lores.pdf
Regardless, if you want audio through your receiver/processor instead of the TV itself, you'll likely still route audio via Toslink/S/PDIF. Unless your receiver/processor has HDMI inputs and video switching.