I would check the Power Settings, "change advanced settings" to see what you might change. Turn off all screensavers to see if that is causing the problem. Screensavers are totally unnecessary nowadays and can cause problems. But since this is new, you must contact Dell asap. This might be something that needs to be reported. Do not let Dell try to make you reinstall Windows (the standard answer when support can't or won't figure out what's wrong) or replace hardware yourself.
Just purchased a Dell Studio XPS 435MT, Intel Core i7-920 2.65ghz processor, 6GB DDR3 SDRAM 1067mhz, ATI RADEON HD4670 512MB,,640GB Serial ATA 2 Hard Drive 7200 rpm, 19-1 W/Dell bluetooth package, Mindows Vista SP1 Home Premium 64 bit, Integrated 10/1000 ethernet, 16X DVD+/-RW, integrated 7.1 audio, Dell 1505 WLAN, Bluetooth keyboard and mouse. Unit works fine when you first power it up, but if you leave it running for approx. 20/30 minutes it locks up. The screen saver freezes in place and nothing works. Only way to get it active again is to manually power down and restart. Haven't been on it for hours at a time, but it seems to work ok if you are actively using it. I've done the self test program provided by Dell, passed. Looked at all settings without finding anything wrong. Except the ribbon screen saver stops working but when the report is sent in Windows does not have a fix for it now. I know a little but not much about computers. Can anyone think of or know of anything helpful before I start with the support people at Dell?