2004 Audi A4 2004 A4 Avant S Line transmission issue

I have 2004 S4 Avant which has a weird automatic transmission problem. Sometime when I start the car, all the gear indicator are flashing. Whenever they flash and if the car still moves, the gearbox does not seem to be "clicking" correctly because whenever I slow down or stop on an uphill slope, the transmission will shake and the car will shut down. In another instant, even when the indicator does not flash, the car does not move as if the gear is not engaged.

In essence, it is quite temperamental because there could be days that the indicator lights up correctly and the car behaves as if nothing is wrong.

My mechanic told me that I have to replace the computer altogether and would not be so sure if the problem could go away.

I am wondering if this is just a transmission issue or really a computer control issue.