Pinched a wire, is this an electical danger?
If you damaged the wire then it is possible it is no longer capable of safely operating under the load that is called for.  This is a potential fire hazard since it may result in the wire overheating.

You should replace the damaged part of the wire.  Depending on circumstances of the wire (which you haven't fully detailed) you may be able to cut out the damaged section and splice the resulting free ends together (or splice a replacement section in to the gap).  You should use proper splice hardware for the task, which could well be a simple wire nut (though this depends on the type and gauge of the wire as well as the service conditions - eg, wet or dry, exposed to oil, gas, etc).

If you are certain that the insulation and only the insulation was damaged (ie, the damage is no worse than would have been incurred had you been stripping the insulation from the wire with the appropriate tool), electrical tape may be a sufficient repair - again, considering service conditions.

It's hard to say whether the damage to the circuit board will result in dangerous conditions or not.  Chances are, everything on the board is sufficiently low power that there is no danger - but with the information available here, we can't say for sure.