If its a 12V battery vehicle, then the ECU is likely to work from 9V until 14V with no issues. That is the usual requirement. So 13.5 is alright.
What make is the vehicle? I believe its a KIA or an Audi...?
Meanwhile, disconnect the battery terminals, switch on headlights to run down any current left, short out the ECU by touching battery terminals with eachother (while the battery is unplugged), clean the OBDII Port pins with Contact Cleaner/Injector Spray. Let it dry for 15 minutes. Reconnect battery terminals, check if there's any corrosion. Apply petroleum jelly on battery terminals. Check wiring from alternator and ground connections. @volkan.rulex