But before you go and replace the switch (which might very well be the
problem) make sure that the relay for the non-working lights (high beams in
your case) is indeed not getting voltage from the dimmer switch.  When your
low beams are on, take a test light or volt meter and with one of the tester
leads grounded to the chassis, you should get 12 volts at the terminals on
the relay: the larger (power feed) wire that feeds power into the relay, the
wire that goes to your low beams, and the smaller signal wire that comes from
the dimmer switch.  Now, flip the lights to high beams and do the same check
on the high beam relay.  If there is voltage at the larger (power feed) wire
only, then it is most likely the dimmer switch (you have first checked your
fuses, right?).  If there is voltage at the larger (power feed) wire and the
smaller signal wire that comes from your dimmer switch, you have a bad relay.

Make sure you check for loose connections also.

Simply:
power at one relay terminal - bad switch, fuse, or wiring between switch and
relay
power at two relay terminals - bad relay
power at three relay terminals - bad lights or wiring between relay and
lights

hope this helps,
Roger