Like holmes4 stated, if you see the Ubuntu splash screen, it's probably a software problem, not hardware.
Next, I have a couple questions, which I hope will lead to the answer.
How large is the SSD
? The smallest 4GB SSD
fills up easily, which can cause problems.
Can you boot into Recovery Mode
successfully? If I recall correctly, the boot menu timeout is set to 0 on the default Dell install, so you might have to mash Escape blindly as the "Dell" splash screen ends.
Or try hitting "Ctrl+Alt+F1" at your "blank, black screen" to attempt to switch to a "Virtual Terminal
". Then you can logon to a command prompt and attempt to figure out the problem. Since I'm worried about the drive being full, I'd start by running "df -h /". "df" shows Disk Free space, "-h" makes the listing "human-readable", "/" tells it to show the root filesystem only. Is the drive full?
If neither option works, you might need to download a Linux LiveCD ISO. Then burn it to CD or use it to create a bootable USB drive. Then boot off the disk/drive and start diagnosing/fixing the problem.
If the Ubuntu install is completely screwed up (worst case), you'll need to install an OS fresh on the Mini (after copying any files off the SSD
to a safe location).