Have you checked the turn signal / combination switch on the steering column for shorts to ground yet?
if my Hazard switch is turned to Turn signal switch ON position, all of the relays in my car pulse
if I turn the switch to the Hazards, everything goes back to normal and Hazards flash
I'm still confused, so when the hazard switch is OFF the relays turn on and off? If so then yes, there is a short circuit on the turn signal circuit somewhere and I agree with NewZed that replacing the hazard switch may have created a new problem whereby the turn signal flasher is now activated with the ignition off and the turn signal switch in the central position (ie. the new hazard switch is wired wrong and you also have a separate short on the turn signal circuit)