When I turn on the left blinker, the hazard lights come on.

I'd check the age of the battery (five years is all you're gonna get from one of these tin/antimony jobs)----get a brand new one, then clean off the other end of the cable that attaches to the frame...as this will be overcoming "weld" forces from the demand of the amperage needs of your starter motor~...co-incidentally is the chassis main ground too----the hazards and the blinkers need to see full voltage or they will not behave properly...this includes supplying GROUND to complete the circuit~

You may have to replace the directional switch.

We have replaced the directional switch and have also bought a new battery as another car guru suggested. We still have the same problem. Any other ideas?

check all of your wiring, especially under the back end. could have wires rubbed and crossed.

here's something~look the the junction blocks~

Yes---your "combination flasher" is bad~------- http://www.moparpartsoverstock.com/p/gb/DODGE__DAKOTA/FLASHER/6 661915/04686795.html?partner=googlebase_adwords&kwd=&origin=pla

achem....that took about two seconds to research....victory dance judge_roy...yesssssss~

I just had the same problem but with the right hand side turn signal. I cleaned the connection at the ground leading from the negative battery cable to the inner left fender and all is better now.