Well, it does depend on where the power supply for the Sound System was sourced as to what actually got overloaded.
My advice, to anyone who listens and thousands who don't, is to
NEVER connect a high current accessory to existing wiring.
It will compromise other systems too much and at worst, cause a fire
The remedy is simple.
Add a new distribution cable from the -ve battery terminal to a new additional fuse distribution block.
Protect this new cable with a Maxi-Fuse, right at the battery post.
Then you can feed power to your new bits from either the new main cable or via new fuses mentioned above.
It doesn't matter whether you retain the original alternator or fit a high output one.
The wiring needs to be separate, dimensioned correctly for the designed load and protected correctly to prevent what you have experienced.
Here is a Wiring Diagram I drew up for a similar question on another forum.
It includes relays to minimise voltage drop and switch power when ignition is switched ON for example.