Your issue is not a broken band.
A broken forward band will make it so that when the shifter is in D or 3 you will have no forward movement. Yet reverse and if you pull to 2 or 1 you'll have movement. Forward movement won't be normal, but it'll move.
Losing all gears after a moment or minute is typically a clogged filter. Our transmissions run on hydraulics, without fluid to the various areas, they simply can't do anything. Hence the loss of all gears and when you turn it off..the material falls from the filter and then you can get moving again.
Something like this could clog a filter
