OK, then 2 possibilities :
1. The battery was a lemon.
2. Cable / cable connection issues.

At either rate, the erect spoiler is an indication of voltage issues.
The BCM controls the spoiler, it detects ( among other things ) the dash mounted spoiler control switch. This switch is a multi voltage switch utilizing a resister to drop the 5 v supply voltage to signal "spoiler down", and full voltage to signal "spoiler up".
When the supplied 5v signal voltage drops ( due to low battery voltage ), the BCM thinks you are calling for spoiler up.

( in event of an erection lasting more than 4 hours, please contact your physician )
ooops - that is an American commercial, you might not get that over in old Blimey.