I recently started having a problem with my L512 running Windows 7 Home Premium 64bit Service Pack 1. It would take an extra two minutes to boot, spending that time in the bios portion (i.e. Windows hadn't even kicked off yet). My laptop also would randomly just turn off - abruptly, no warning.
I finally narrowed the problem down to an optional Microsoft Windows update named "Intel Corporation - Display - Intel(R) HD Graphics", released November, 2010. My problems began after I installed this update. The reason I noticed this update is because of an update in the Lenovo ThinkVantage Tools - Update and Drivers named "Intel(R) Graphic Device Software for Windows 7 64bit" that wanted to be installed, but didn't want to because it complained there was already a newer version installed. I forced the installation of the version in Lenovo ThinkVantage Tools - Update and Drivers, and the problem disappeared. The "Intel Corporation - Display - Intel(R) HD Graphics" update in Windows Update then reappeared, but I hid that one, since it causes problems.