This is a regression from Mint 17.3, where suspend/resume worked just fine on that same machine (using a series 4.2 kernel -- Mint 18 comes with a series 4.4 kernel). Any ideas?
I have a brand new Dell Precision 5520 and am running Ubuntu 17.04. After suspend, when attempting to resume by pressing the power button, the machine would reboot.
I was searching, trying to figure out what caused this and came across this thread. I checked my BIOS and was at 1.2.4. Dell's latest was 1.3.3. I downloaded and installed. Resume now works as expected with Ubuntu 17.04. I suspend and after the machine sleeps, I press the power button and it resumes back to the Ubuntu login prompt (which it displays, then the screen goes completely black for a moment, and then displays the login prompt again). After entering my password, I get back to the desktop in the same state I left it in before I suspended.
First, check if you are running the most recent BIOS. Depending on the hardware, this may fix a lot of issues and you also need it to file a bug report.
I am not sure about which Ubuntu version Mint 18 corresponds too, but if you have a standard setup, and the problem persists, you can file a bug report on launchpad. Please update the BIOS before doing that.
There is also a patch in the waiting, maybe you have to await that: https://patchwork.kernel.org/patch/9402601/
or apply the patch yourself and compile a kernel as described (just Google, I can only post 1 link because of reputation). Check the bug report mentioned there, you may be able to help out.
You could try Dell support too, because it seems like a BIOS bug, but they would have to support Linux on it to be able to help.
Please post how it goes, good luck!