Have a 2000 Blazer 2 door LS and was at the dentist's office and when I came out an hour or so later I go to start the Blazer and the battery was clicking almost dead, but I could hear humming from the fuel pump. Not loud as when you put the key in to start but still humming away. Ended up having it towed home. Fuel pump runs all the time and stops after I pull the relay with ignition on or off does the same same.Swapped relays and no difference. Just happened all of a sudden. Any ideas? I don't have any. Thanks in advance. BTW..Can they do exorcisms on Blazers?

 

Maybe your oil pressure sending unit, some have a shut off feature, lose oil pressure it shuts off fuel pump so engine doesn't run without oil circulation. When they go bad they can have the opposite affect.