Computer to hd tv?

I do this all the time with my HP laptop. Not sure what a DP output is honestly but it's possible with a Mac. Obviously straight HDMI would be the best because you would retain the sound, but I don't think Macs have that output? Anyways just get the image however you can, I use VGA, it gives perfect quality. I know there are Mac Output-to-VGA adapters. Then what I do for audio is plug a set of 2.1 Logitech Speakers into the laptop's headphone jack and it gives great sound.

forgive me , I don't know much about mac's, or even what "DP" means. I can try to help. If you have HDMI output on the computer that is your easiest and best bet. You will be able to run up to 1080i/1080p with sound with hdmi cable. 
A lot of older computers don't have HDMI out, your next best bet would be a VGA cable, (monitor cable) , that should get you 720p, but no sound. You can use a simple line in audio cable with computer speakers/surround , just plug it into your line out/headphone jack and you should have stereo sound.
Another option is if your tv and computer have an S-video cable, not going to be the highest resolution and will remain without sound unless you use the the line in cable i mentioned before.
I do think they make a dvi to hdmi conversion cable that might work as well, not sure about the quality or sound with that. Hope that helps out a bit.