Help!!! transmission trouble

Recently bought a 2005 golf tdi automatic to make into my daily driver (this is my first vw), car will not shift out of first gear and has check engine light. upon getting the car back to my garage i discovered tranny hadn't been serviced properly. i properly serviced the golf and was hoping this would help get the car driving while i gather parts needed for swap but no luck. it is a theory of mine that due to being in properly serviced that the car put itself in to safe mood to protect itself. is there anyway i can test this theory. i was aware of a transmission problem at time of purchase and plan on doing a swap but was hoping to get it driving for a month or two any advice or theories would be appreciated.

as far as i can tell everything seems to be original.

OBD works, start there.

There is no SAFE mode due to not being serviced that I have ever heard of. It will go in safe mode if there is a failure in the transmission so it can be driven a few miles. Get a scanner and check for codes like oilhammer suggests.

If it will not shift out of first gear, chances are it is not in "safe" mode, but has a shift solenoid or valve body problem.

Try driving it when its running up to speed in first, shift into neutral, shut the engine off, then restart it again and put it in drive-not the safest maneuver, so do it where there is no traffic if possible. Sometimes these will have a first-second shift problem, that when you do the check I listed causes the TCM to bypass second gear and go right to third when you restart it and put it back into drive. If it shifts into third after shutting it off and restarting, its most likely a valve body or shift solenoid problem, in my experience.

plugged it up to a reader and the only code its showing is a transmission code "implausible signal"

You need a better scan tool, or at least give us the rest of the DTC in its whole alpha-numeric form.