The cheapest route is probably using DVI to HDMI cable for the video and a Toslink/Optical cable for the audio.

However, 45' is pretty long. Is that a straight distance? My HTPC is almost 20 feet from my HDTV/Receiver and with a 35 feet cables they barely reach the devices and had to carefully manage the route due to wall corners and doors.

50 feet DVI/HDMI cable runs about $66 at monoprice (link) and a 50ft Toslink cable about $12.

Alternatively, if you have a PS3 or XBOX 360, you can use that a media server.
You might also want to check MViv MX-780HD.