Why does my ford taurus stay in first gear too long?

2000 Ford Taurus ses when I start it up the doors don't lock, the speedometer doesn't work and it stays in first gear for a while and then seemingly randomly( hot cold running a long time or just started) it'll eventually kick into the next gear the doors will lock and the speedometer will work but sometimes it takes a really long time

Fix the speedo and your fix all the problems. Maybe the sensor on the rear output of the trans has metal shavings on it and keeps it from working.

I would bet that it it all related to the speed sensor.

If the sensor is sending data due to a bad sensor or bad electrical connection, the transmission doesn't know when to shift, the doors don't know when to lock and the speedometer gets no data.