S3 making a clicking sound, won't boot

It is common for the capacitors in the power supply to fail, or about to fail and they all need to be replaced.
If you do not have the ability, find an electronics repair shop in your area. You can also google it with your location.

After that, you may also need to have the hard drive replaced. The drive needs to have a matching model image on it to work.

 

Second ThAbtO's comment on capacitors & repairs.
The capacitor on the left in the photo looks bad to me.

 

Capacitors are a easy and inexpensive fix... if you are replacing one, it's a great time to replace as many as you can because others may be close to failure too.
That capacitor in front of your transistor looks like it may be next to go bad? Look for ANY sign of bulging at the top and any sign of black/dark brown chemical within the "X" on top of all electrolytic caps... replace these first.

Also note the condition of your thermal paste on your power transistor? It appears to be old, cracking and perhaps has seen it's better days? That paste tends to crack and cake with age. Carefully clean the mica wafer and install fresh paste. Unsolder the transistor to really spiff things up... (that mica is thin and delicate... please use care).

SOGLAD