Dell laptop will not turn on (at first).

Did you try disabling IME?

No. How can I? Uninstall it?

In device manager - Right click|Disable

This is what I disabled (the highlighted one). Correct one?

Yes.
If it works and you don't like running with it disabled you can try other drivers, some people have had success with some v9 ones, I didn't.

EDIT
Please post back with result.

I think that fixed it. I'm going to try different ways of shutting it down and see if I still have the problem. I'm still reinstalling Windows 7 but at least I know what the problem is should I dual boot with Windows 10.

Good, hope it's fixed, but as you most likely realise by now the problem can hide away somewhere and then reappear after a day or so.

So, after a couple days, I no longer have the startup problem. When I do the clean install of Windows 7 and then install Windows 10 (dual boot), how can I be sure to not have this issue pop up again? Install "IMEI" and then disable it or don't install it from the beginning? Would it be installed when Windows 10 updates?

It will install, whether you uninstall or disable it is up to you, I disabled it so that MS don't have the chance of seeing it missing and installing it. The 1511 update enabled it as I imagine 16mm will when it arrives.