I had the same problem. I found the answer in the EA Customer Support area. Here's a link but it's crazy long and I don't know if I trust it'll remain valid:
LinkIt's a pain but following the instructions fixed it for me. Just in case the link doesn't work I've copied the instructions below.
(copied from EA's customer support site)Windows Vista users with UAC (User Access Control) enabled may experience a crash to desktop when running Mass Effect after installation.
The solution to this problem is to disable UAC, run Mass Effect PC once and then enable UAC on your Windows Vista Control Panel. Once the procedure has been completed, you will not have to repeat the it unless Windows Vista is reinstalled.
Detailed Instructions:
Open Control Panel.
Under User Account and Family Settings click on Add or Remove User Account.
Click on the user account you would like to disable UAC for.
With a user account selected, click on the Go to the Main User Account Page link.
Under the Make Changes to Your User Account heading click on the Change Security Settings link.
Under Turn on User Account Control (UAC) to make your computer more secure uncheck the box beside Use User Account Control (UAC) to help protect your computer. Click the OK button to accept the changes.
Windows will prompt to reboot the computer. Save any open files and reboot to apply the changes.
When your computer has rebooted, launch Mass Effect PC and then exit the game.
Now repeat the above steps but check the box mentioned in Step 6 and reboot when prompted to complete the procedure.