Got it running with a new power supply.  Thanks everyone for the help. Had to get a $100 power supply from best buy but it is workin good now.  thanks again!

What type of power supply do you think I would need?

http://www.ebay.com/itm/390426861734?ssPageName=STRK:MEWNX:IT&_trksid=p3984.m1497.l2649


That is a link to the power supply that I bought on ebay.  it said that it could run 2 x16 cards so I thought it would be ok. Could the power supply be the problem?

I don't have any extra hard drives or CD-ROM drives running.  
I am also running this computer with no case sitting ontop of a desk.  Could this effect GPU Mining?  I can upload pics if necessary. 

Thanks for any help in advance.

Yes I have turned off all the sleep modes in bios and have set high performance in power management with hibernation off.

My computer turns off when I start mining using GUIMiner.  I am running windows 7 with a radeon 5870 with driver version 8.961.0.0 .  I am trying to connect to Bitclocker's pool but will connect to any pool if it will make it work.    I can see it mining for a second before it turns off.  I have programs to monitor the heat temperatures and nothing seems to be overheating. What am I doing wrong? any help would be greatly appreciated.

I'm not overclocking yet, just trying to run it normal. I have a 500 watt PSU and only one video card so I would think that the power supply is good.  It said on the site that I bought it from that it could handle 2 x16 cards.  I am running a MSI 870S-G54.  It does not blue screen it just resets.  But when it resets it stalls on the first screen that comes up and I have to reset before I can get it to load.  Really frustrating. 
I have used GUIMiner,phoenix 2.0, and CGMiner.  I have also tried using Linux and windows with all the different miners.  all of them do the same thing on linux and windows.  They start mining for about 1 second and then the computer turns off.

Thanks in advance for any help.