Download it here and burn to a CD.http://www.memtest.org/#downiso
It's an ISO image. Once it's burnt, reboot your computer with it in your CD drive, set your BIOS to boot from the CD. It boots very quickly and starts to run the default test. Let it complete a few passes, the more the better. I have found that it may take several passes before it starts to error, or you could get lucky and it starts to error right away. Obviously if it doesn't error after many passes, your RAM is fine.
That all said, slow boots aren't normally a result of bad RAM. Usually bad RAM shows up in random lockups/reboots, BSOD's, application crashes, etc. It couldn't hurt to run the scan anyway though. One thing I have found with slow boot/shutdown problems is usually related to network problems. You could try looking in your Event Viewer and see if there are a bunch or warnings.