I have a 2001 S10.

Sometimes when I try to start it, it might take 2 or 3 times for it to start. Sometimes it takes 5-10 minutes.

It doesn't click or turnover and the lights do not dim.

It has a new distributor cap and rotor.

I read that the ignition switch connections might be dirty but I don't know how to get to them.

 

Look for an electrical connector on the steering column, unplug it. It will be a fairly large connector, use a quick dry electrical contact cleaner.

 

Is the connector near the ignition?

 

Follow the column down under the dash it will be there.

 

I found it and the connections look clean.

I noticed the dome lights dim when I turn the key.