Both front turn signals not working...?

I just purchased an '03. Both front turn signal lights are out; the previous owner said they'd burned out a few weeks prior, and seemed to think they didn't both blow at the same time. At $3.50/pr at autozone, I didn't make a fuss. But after I replaced both bulbs (they were indeed blown), the flasher still ran fast, and only the rear turn signals were blinking; nothing out of the fronts. I checked the bulbs, and they're still good.
FYI, no DRL; Autozone tried to sell me the wrong bulbs until I clarified that.
Any ideas on what's going on here?

You may have bad contacts in the sockets.
You need a meter at this point or a tester light at minimum.
check the wires for voltage on the BACKSIDE of the socket, use a small sharp probe tip to puncture the insulation. If you have no voltage there then trace it back, this will require a schematic.
You may have bad contacts in the sockets.

I think you need to replace your flasher relays and check your fuses. Here's what I found for you. LINK Link removed by Moderator - spam

I think you need to replace your flasher relays and check your fuses. Here's what I found for you.

If the rears are working, the flasher unit is good.

You need a DMM and a wiring diagram and start checking from the sockets on back. Also check the grounds.