So I'm currently not getting power at one electrical receptacle. At the switch for this receptacle gets some power because my tester dimly lights up. This is an older house, so no GFCI outlets or reset buttons. The only thing on this breaker that I'm aware of is this switch and the refrigerator. I was currently installing a light fixture and was running it to the switch and this happened. I'm confused...

Sounds like a loose connection somewhere, most likely at the device you were working on.

Well, currently nothing is hooked up. No light switch, light fixture. I pulled out the electrical outlet and the wires aren't getting power either. So I'm thinking about cutting the wires fresh to the outlet to see if this could help. Still lost though.

DIY...
Guessing is not the answer...
Start at your receptacle and work backwards. (I would recommend using a solenoid type of voltage tester because it's fairly immune to false readings, commonly know as a "Wiggie")
Receptacles are frequently supplied from other receptacles so carefully testing all other nearby receptacles might help.
Verify that all your fuses/circuit breakers are on and working...
If you just want to "get it done", hire a good electrician.