Hello and welcome to JustAnswer!
It does sound like the ECM has failed because of this. Unhooking the battery cables with the engine running caused a large voltage spike which has done internal damage to the ECM. The battery is needed to smooth out the highs and lows of the charging system output, unhooking it has either allowed a small spike or it allowed it to quickly overcharge and damage the ECM. The alternator is capable of near 60 volts of output in some cases.
In your first question you said "removed the battery cables while the engine was running to make sure it wasn't charging". Now you're saying that you didn't remove the cables with the engine running? Either way if the ECM blows a fuse when plugged in but it's ok when it's unplugged then an ECM problem seems likely. If you didn't remove the cable with the engine running then some electrical testing may be in order before the ECM is replaced.
I'm a full time tech and I'm at work this morning. If you reply back there may be a delay before I can get back to you.