Is there anyway I can have my computer on, but the power led off?

usually yes, the led is connected to the motherboard by some thin wires. Just disconnect them. There are often 8 wires that go from front of pc to motherboard, 2 for each of Power LED / Hard disc LED/ Power button / Reset button. There are sometimes one push on connector for each wire, sometimes there are four double connectors and sometimes one 'block' with all wires in it - if all in one block you will need to cut the wires

I have a few questions since I am not a hardware expert. What would be the proper way to cut/disconnect the wires? My computer has 2 colors for LEDs, Blue and Orange, is there a way to make it where the orange one doesn't work, but the blue one works?

Odd request but yes, it can be done. You'd have to open your case, determine which wires are used by the LEDs, then trace them back to the motherboard & unplug them.

If you can see behind the front panel from inside the case, or you can remove the front panel to see which lead connects to the blue led, it will have color coded leads which should be a different color from the orange led, you can then just unplug that lead from the board. If you want to use the orange in place of the blue, unplug the blue one and connect the orange in it's place. LED's only work one way, so if you plug it in the wrong way, it won't work untill you plug it in correctly, no harm will be done to the led as current can only flow in one direction in it.