How do I convert a pdf for a good presentation on an HDTV?

I just want it to look as close as possible to the original document and I can't seem to get it there no matter what I try. It's a design presentation that is full of subtle colors and layouts that rely on accuracy. Colors are washed out, type isn't crisp, it's all generally muddy and doesn't look like it does in Illustrator on my desktop monitor (iMac).

It's not in CMYK.

I'm either casting the pdf or going directly through an HDMI cable from Apple laptop.

Saving out of Illustrator to pdf.

Thanks!