Why my Nikon SB800 speed light explodes during photo shoot?

I had a 3-day photo shoot, about 6 hours and 400 photos each day. I used 5 Duracell Ultra Advanced and an rechargeable external battery, everything was fine until the end of the third day, I switched to Duracell Quantum, after 10 shots I heard a "pop" and I saw the plastic melted a bit. I was able to turn the speed light on and off and see all the functions but the light is gone.

I'm not sure what happened. Was it battery issue or my speed light is over used? Also my speed light is about 10 years.

And can I have it repaired?

Your professional advice is deeply appreciated.

I suggest that you take it to Best Buy. They usually accept electronics for recycling.
No it can't be repaired. You seem to have gotten a very reasonable amount of service from that unit.

It wasn't because of the Quantums.

Quantums are Alkaline, as are Ultra Power, and there's maybe 10% more energy in the Quantums, depending on the discharge rate. Otherwise they have the same voltage. The extra energy just means they would last a bit longer.

I just think your speedlight was ready for retirement.

2 possibilities:
1. The discharge tube that generates the light doesn't last forever. Just like the light bulbs in you house. This is easy and pretty cheap to replace but get it done by a repair shop. There's a capacitor in that gun that can give you a very nasty electric shock even if it is "fully discharged"

2. The capacitor has failed. Was there any smoke and a nasty smell? If this has failed then it will have taken the circuit board with it and it is probably not worth repairing.