I've tried researching intensely to find out why every time I try to boot my server, my monitor that I use to see what I'm doing to the server, seems to say "Out of Range".
I have Ubuntu installed and it was working fine until I messed something up. I've tried booting into every OS it has listed in the OS selection options, nothing helps.
What's wrong? (Or could be a solution)
The server you're describing is an HP ProLiant DL380 G3 from ~2003.
That means that you're working with a 12 year-old server, so there's ALWAYS potential for hardware failure with something of that vintage.
The positive side is that you have a Integrated Lights-Out (ILO) interface on that server. The ILO will allow you to control the machine and see the screen without needing a monitor. If you haven't already configured the ILO, I guess it'll be tricky without a monitor... but it's worth trying.
Have you tested with a different monitor?
Edit:
Ubuntu doesn't belong on hardware sometimes... You probably ran updates and need to change the video mode. Please see this post for help on how to edit Grub to resolve this. Also here.