Two of the BSODs in particular that you have gotten stick out of the pack. Namely the one concerning the file ntfs.sys and the other being SYSTEM_SERVICE_EXCEPTION. These two alone tend to make me think that the partition table is either corrupted or has been infected with something.
I understand that you mentioned that you created an image using LiveDisk but that cannot be considered a clean install due to it essentially just cloning the installation (and the aforementioned problems).
You may have to go as far as attempting to acquire a Windows 7 CD or contact Lenovo in order to get one and go in and take out the OS partition and then re-build it.
The source of this could be a bad image load from the factory and there is no true way to fix it using the Lenovo eRecovery because it essentially will load the same suspected bad image.
I'll look around on the Lenovo site for you and see if I can dig anything helpful up. If I do I will edit this post.
UPDATE: I'm assuming you are state-side so here goes. The best option would be to contact Lenovo Support and see what options you have as far as obtaining a OS CD for the computer. If they are not willing, there are "methods" of getting a Windows 7 iso in order to redo the system and still use your product key.