1999 Chevy Blazer Intermediate Starting

Ocasionaly the ignition will not do anything, of course this happens at the most inconvenient times.
Turn the key and absolutly nothing happens. All the electronics work, i.E. Lights guages. The next morning it starts up with out a glitch. I've replaced the battery, thought that might do the trick but to no luck. Then it will work fine for a week or so.

Frustrated in Philly.