[villagetinker]

There are several versions of under cabinet lights. Put your hand near (do not touch) the lamp or a similar one, if it appears to be hot, this is an incandescent or Halogen bulb, and yes, they can typically be replaced by the homeowner. Once again depending on the manufacturer you may need a screwdriver to get the cover plate off. NOTE: if this is a halogen DO NOT DOUCH THE BULB with your fingers, use a paper towel to install the new bulb.
As mentioned if you have strip LED lights I have seen the snap in connectors fail and the lights blink. You can easily test this by applying pressure to the snap connector, if the LEDs come on or stop blinking the connector is bad and needs to be replaced. I do this type of work, and I solder the bad connection. I have a whole box of unused snap connectors that I refuse to use because they tend to fail.
Also, I agree with above, a picture would be very useful.
Send me a PM if you would like to discuss further, I do not post email or phone number on open forums.