Re: Debian Wheezy on Dell 7535
What happens when you shut down from a boot DVD (life CD) Linux ? Like GRML oder some installer disk.
If that works then try to install the same kernel.
Anyway, does it work from Windows (does the laptop still have that ?), and can you do the Dell hardware check ?
Should be onboard, otherwise try support, like http://www.dell.com/support/home/us/en/19/product-support/product/inspiron-15-7537/diagnose
(this was the model closest to your 7535 that i could find though)
Maybe it's worth to look into BIOS and switch off some IRQs or ports that you never need...
If even Windows does not shut down then it's probably a warranty case.