X120e does not sleep when lid closed

Question

I found another similar post, however it was resolved by the individual reinstalling the operating system.
My issue is more complicated. I have made sure everything is up to date, all the settings that tell the system to sleep when the lid is closed are turned on. I have even turned those settings off off, just so I could turn them back on to make sure there wasn't something quirky about it.
I have tried restoring the system to factory settings using the recovery partition, as well as discs burned from the program that came with the computer. I have tried clean install from Windows 7, 8, and 8.1 discs.
The unit still does not sleep. I don't ever remembering it being able to. I once closed the display thinking it would sleep (power was plugged in). Woke up the next day, went to work for 8 hours, came back and felt that the system was really hot. Opened the lid and the screen was exactly as I had left it the day before.
When I first got the system in 2012, the screen did not work, so I actually had to send it to Atlanta, GA for repairs. It came back quickly, and it still did not work, so I actually sent it back to Atlanta, GA's repair center a second time in the same week. It came back working and I left it alone. I never tested the sleep/wake because I always just turned the system off when I was done with it, but now I am back in school and this little computer comes in handy, but I don't want to turn off the system manually going from class to class when I need to pack it away in my bag.
Could there be a hardware issue? Something inside not connected? This laptop works perfectly EXCEPT for the fact that it will not sleep when the lid is closed. It is out of warranty but had I known this was an issue while it was still under warranty, I would have inquired. This unit is in pretty fantastic shape, looks brand new too. No damage, never been dropped, and only ever handled by me (never loaned out).
How can I fix this?

Answer 1

Thanks for the reply, gat0gelat0.
Yes, those settings were the first things I checked. I also tried changing it to "Do nothing", then changing back to the sleeping option. It still does nothing when I close the lid.
I would like the functionality of it going to sleep when I close the lid for the convenience, like when class ends, I have to rush to my next class, I just want to close the lid, put it in my bag and run to the next class. Keyboard shortcuts like Fn-F4 work, but this laptop should have the functionality I am describing, and I want to figure out why it isn't working and how to fix it.
I suspect there is an issue with whatever is used hardware wise to sleep the machine. Either it's not being triggered, or it's not there, or it's broken. I've tried running a magnet around the bezel of the LCD screen as well as around the palm rest bezel and there is no activity as I've read that many laptops trigger sleep by interaction by a magnet. Still nothing.