Assuming the battery isn't defective something must be drawing power from it when it is off. The likely source will be the additions from the previous owner. Try disconnecting these and see if it helps. Generally things like stereos should have two power feeds, one from the battery (through a fuse box) and the other from the ignition (acc or accessory). The stereo draws its power from the battery and uses the acc signal to tell it when to turn off. Sometimes people install these incorrectly with the acc wire on the stereo or amplifier connected to the 12v line. Amplifiers also should have a signal line to the stereo to tell it when to turn off, this may also be missing? Do you have a multimeter?
It's possible the battery you used doesn't have the capacity it claims to have. Also the blades could need some oil or be blunt making the motor work hard and the battery last less time.
Those batteries should be fine. Whilst I don’t know what the blinking LED means (it may be in the manual) I would check the following;
The batteries are around the correct way.
There isn’t any excessive solder creating a short circuit .
If you have a multimeter, check the voltage of the batteries with the unit unplugged. You may have got a dud battery. Ideally you should have charged them both before installing, this would have ensured they were both at the same charge level.
The metal tabs pictured at the top of step 6 aren’t bent etc.
Be careful with it apart, you may be familiar with electricity but please keep in mind there will be voltage exposed on the board which is capable of killing.
I’m not sure that helped much to be honest, feel free to post some close ups of your soldering and we can see if there is any issues with it. I doubt you have done any permanent damage.