When I turn on my light switch, there is a delay before the light comes on
This is one of those problems that you just have to work out systematically, don't be swayed by logic. 


If there is only one bulb change it.
Check the wiring at the light and switch - see that the connections are tight.
Change the switch.
Try wiring a test lamp to the fixture.
Call an electrician. You may have serious wiring issues.