My lighting timer seemed to have burnt out. We thought that the switch was bad, because light was out - replacement one does not work either.

If I understand correctly you installed a new timer and it does not work.
You posted under EJ351 timer.

Problem sounds like it's electrical instead of timer.

1) Check electricity at wall box where timer is located. Remove both wires from timer. Separate wires for testing. Turn on power. Test each wire to bare ground wire. If box has power, then one wire will light up tester. This is Hot wire. Next test Hot wire to white wires inside box to make sure circuit can be completed to the neutral. If box doesn't have Not or Neutral then check other local boxes on same breaker to find where loose wire is.

2) Check that Load (light, fan, motor) is not burned out ... you can do this by putting regular light switch in place of timer. Box must test positive for Hot and Neutral wire.

3) Check that breaker is delivering 120V. Test from screw on breaker to any bare copper wire inside breaker box. Tighten screw on breaker. There is a white wire associated with black wire on breaker ... track this wire over to neutral busbar and make sure it is tight.

4) If electricity checks out, then timer is suspect. You may have gotten bad timer.