If you're getting
the solid click of the solenoid pulling in,
and not a continuous clicking when the key is held at START,
and the dome light doesn't dim way down at the same time,
and still no starter motor action,
then the starter motor isn't being connected to the battery through the solenoid.
You can verify this by measuring the Voltage at the large post on the solenoid that the positive cable from the battery is connected to. When the key is turned to START, this would normally drop a couple of Volts (from where it was just before, which should be around 12.7 Volts for a fully charged battery) if the solenoid contacts are connecting to, and through, the starter motor.
If the solenoid contacts were badly burned earlier, it's possible that the starter motor is failing, and was drawing too much current causing the burning. The new contacts might have helped for a while, but with an unusually heavy load, might have deteriorated once again.
The starter motor can be tested to see if it's drawing excessive current. Worn brushes and/or a dirty commutator are not uncommon. Also, a bad contact between a brush and the commutator can give the same sort of no start, no start, then start, symptom.