You clearly are in over your head and need to call an electrician.

Sounds like you installed a receptacle in a light switch location.

If you want to do some more sleuthing, get two circuit testers - one with a light and two wires, and a non-contact one, and trace out your circuits.

The first rule of troubleshooting is to find out why the power isn't getting there in the first place. You may have replaced a bunch of switches and outlets without needing to the first time around, because the breaker was bad. Possible you miswired something in the process.

First you should verify that you wired everything correctly. Someone suggested a circuit tester, that's a good idea. Find out which lines are actually hot. Are the switches actually switching a hot wire? Are the outlets wired with black = hot and white = neutral? Verify all that first. And be careful with the power on and wires/terminals exposed!

Do you have a GFCI outlet in the bathroom? Or is the breaker a GFCI?

Your fan may have a bad motor or bearings, and it was just time for it to stop working. In fact, if it turned slowly and dimmed the light, it may have been drawing way too much power (a short). Try disconnecting the fan and see if that helps anything. I'm just spitballing, which is probably not a good idea but none of these tests will hurt anything if you're careful.

Or, yeah, call in an electrician.

You mention that after changing the switch for the fan, the light comes on but very dim. Was it coming on before you changed the fan switch? Try plugging a lamp or two somewhere in the circuit. Try in several locations. Does it have an effect on the brightness of the fan light? If so, it is quite possible that you have installed a receptacle in place of a switch. If that's the case, all the current from the circuit goes through whatever is plugged into that receptacle, and if nothing is plugged into that receptacle, the circuit is open and appears dead.

When you replaced the fan switch, how many wires were going to the old switch? Are you sure you have connected it properly?

Did you notice any wall switches that used to work but no longer seem to do anything? Perhaps you had a duplex receptacle that was half controlled by a switch and you forgot to break the tab on the new receptacle?

I had a similar problem last fall. Does it begin working again after you use an appliance/ system with a high draw? It might be cause by a line into the meter or panel box. Call the power co. to come out and check their line in. If that checks out, call an electrician. mine was a frayed wire inside the conduit on the side of the house, between the pole and meter.