No Electricity To One Room
The pen looking tester should light up on the smaller hole (if the ground is down it will be on the right, the outlet tester won’t work if the hot is open someplace).
The pen is called a non contact tester (it sometimes gives false positives).
What I usually find is the circuit was overloaded or heavily loaded and a back-stab connection failed (as in, 90% chance that's it), after that, it could be that a wire nut is loose, a broken wire, or a bad wire in the panel.
I start by working my way back to the breaker panel, identifying all the dead receptacles. If I find one that seems to be on that circuit that is working, I turn off the breaker; if it turns off you will be close.
A failure in a daisy chain is always at the last working or first non-working device. Remember that a receptacle could be on the other side of the wall, yet on the same circuit.
Identify the last working receptacle or switch, pull that out, and look for a loose wire or burned insulation as a bad connection may damage the insulation or burn the wire off on either the hot or the neutral. If you don’t see anything, put the last working one back in and turn the breaker back on. If everything starts working and back stabs were used, the failure will happen again; use the screw terminals or replace the receptacle.
If it is still dead, turn the breaker off and check the first non working receptacle as it will be in one of these 2 places +98% of the time. Broken wires from nails are rare but possible or a loose pigtail in those locations can also happen, but bad backstabs are so common that you will find this advice hundreds of times on this site.