Car will hold back when cold to protect itself.
Screeching; what condition is the AUX belt / tensioner / Alternator pulley in? You can self test the Alternator pulley, by using an open ended spanner on the tensioner, pull towards the front of the car, place allen key into lockout... (ideally battery should be discconected for next step)... place thin screwdriver into alternator to stop blades turning and then turn pulley backwards and forwards, it should lock on way and freewheel the other... if it's locking both ways or freewheeling both ways it's goosed... £30 part and £10 belt.