[mustbeme]

Just installed a new battery. Old battery looked old from prev owner and gave out after some ignition symptoms. Now New battery and:
1) Nothing in holding run position no noise buzz nothing
2) then starter will engage and I can let go of key and starter keeps going
3) Engine will crank and run but after shut off I must pull the EFI relay to attempt a restart almost like "resetting" something
4) Some buzzing from Throttle body area, I can pull plug there or pull the EFI relay and make this stop

I have swapped the EFI relay with others and same result. Is there some other ignition component to check?

[riceandpho]

any aftermarket stuff installed? sounds like an aftermarket alarm, starter kill installed, maybe your key is not being recgonized by the transponder.

[MikeinNH67]

Any odd lights on the dash? As mentioned, immobilizer may be stopping it. I think there's a light that goes off after a short bit if the key is recognized but I'd have to look to see which it is.

[mustbeme]

Update: TPS/throttle body is continuously making noise and killed the battery overnight.
Getting TPS code in scan tool. I can pull the blue relay (EFI) under the hood and she usually fires right up. I ordered a replacement TPS/throttle body

I cleaned grounds, pulled fuses and clean and inspected. Hoping a bad TPS. I have not bench tested it. Don't have a manual. Thanks for the replies. Will update what I find out.