Okay, now that paints a lot more cleaer picture for me...
I would therefore recommend the following:
if tank A has two filters running, take one of them and replace it with one of the filterd from tank B, coz you know tank A filter has enough BB to support fish...
If it only has one filter, then take some of the media (such as bio rings) out of tank A filter and place it directly in tank B's filter to kick start a new BB colony asap...
Also i think your problem initally was that you left the tank running for 2 weeks with no fish in it, therefore killing off any BB because there is no food source for it to live off... then when you did go and add new fish in, the tank was basically un-cycled or un-fit to support fish...
Fishless cycling also does work but i've not done it personally so cant really comment if it was done correcrtly as i've always taken more media than i need to start up new tanks and pretty much stock the tanks right away...
Anyway, thats my 0.2 cents on what i think happened