I had the same cold start issue with my eng. and it went like this.

Wouldn't fire when cranked until I depressed the pedal just a little bit.
Then I had to hold it that little bit until it warmed up a little or it would idle so slow it would die. Once the eng. was warm it ran fine.

The cold start injector only assist in geting it running so I bypassed that and went to the coolant sensor (notorous for failing) and that was the reson I had no cold running enrichment.

That is the easyest to Diagnose and cheepest Idem in the fuel system too.

Do a search for coolant temp sensor testing.

I also had the same prob. with seat switch only I wasn't able to get it cured with the contact cleaner so I had to disasemble it and clean the contacts
it worked great.

Good luck.............