I keep trying to turn it on the green light comes on then immediatly turns red, and I think it might be because someone unplugged it while it was on.
If your Xbox is writing to the hard drive when it is unplugged, then yes, you can do damage.
The way most hard drives work, you have lots of spinning discs on top of each other. When the Xbox writes data to it, it is putting down bits of data in a scatter across these discs, and when it reads, it spins them around quick enough to be able to move between bits in the order they have been put down, regardless of how efficient the bits have been ordered.
If power goes out during a write, you can end up missing some of those bits. The file then becomes incomplete, which can lead to hard drive corruption.
When the hard drive is in use, you should never remove the hard drive, cut power, or move the Xbox.
There is an easy way to test it. Take out the hard drive, and see if your Xbox will turn on.
If you feel around the vent filling the left side of the console, you will feel a small patch that is not in line with the rest. This is a latch that removes the hard drive cover. Make sure your Xbox is off and unplugged, and remove the hard drive. The easiest way to do this is pulling on the fabric tab that hands out. Once your hard drive is removed, turn the Xbox on again and see if you are still having troubles.
Please note that this is instructions for the most recent Xbox 360 model, but other versions of the console should still have a removable hard drive.
If the hard drive is giving you the red ring, your Xbox will run normally once it is removed.
I had the same problem, myself, but this fixed it.
In addition to Timelord's answer, another issue that could be caused by an interrupted power source doing damage to your system can be seen here.
To summarize: When your Xbox is off, the power pack has a little orange light when turned on, this light (should) turn green, and your Xbox will turn on. If the power pack is damaged, that light will instead turn red, and your Xbox will not turn on correctly. If this is the case, this is likely to have been caused by either a power surge, or an unexpected cut in power.
It is entirely possible that the power connection is not correctly set up.
The Xbox Support page has a few solutions for this issue. The general consensus is to either:
Turn off the Xbox and the power point, then disconnect all the cables - from the power source, from the power point, and from the Xbox, then re-connect them all. Make sure they are firmly connected before turning the system back on.
Try it in another power point. It's possible the power source is not providing the Xbox with enough power.
Remember - It's always good to use a power-surge protection for electronic devices.