The flasher solenoid has gone bad. Had the same thing happen on my 99. The flasher is NOT under the hood, it is behind that kick panel that is below the steering wheel. Pull that kick panel, and the metal plate that's behind that kick panel (which comes off when you unscrew the plastic piece) off and you'll see the small box that is your flasher solenoid. If you are unsure, turn the ignition on and turn on the blinker, and you can hear (and feel) which is the one for the turn signals. I believe there is only one solenoid in that general area, but it's been a while and I don't have my FSM handy so i can't look it up for you.
I'd advise going to autozone to get the replacement....shouldn't cost more than $3 or so...atleast that's what I paid for mine.
I say go to autozone becuase when I went to Napa, they told me "that's a dealer only part."
The one I got now has a slightly faster flash to it, but as long as it works, I don't care. It's been over a year now with no more problems.