Ok here's update:
I did reflow the solder on analog board and no success. It doesnt give me a boot sound anymore. I can only hear internal fan and HDD spinning.
What should I do next? Which one is more likely to require a recap - power supply or analog board?
If it chimed before you resoldered and doesn't now, the first thing to do is check what you touched.
* Really silly question - did you plug the sound back in?
* Inspect your soldering - share a photo
* Check all cables are seated correctly
* Reflow the solder on all of the molex connectors that go to the analogue board again, plus the solder pads on the flyback transformer. I know you've already done this, but your initial symptoms are straight up, good old fashioned "stupid dry solder joints"
* Possibly reflow the of the power molex that goes into the logic board too.
The powersupplies are pretty solid on those - given it chimed until you did some work on it, it is more likely to be due to disturbing it than the PSU failing by coincidence. Although it isn't impossible.
When you're reflowing the solder, use some "no clean" flux. It will make sure you get clean, healthy connections and you wont have to force so much heat into the connection to get it. Make sure your iron is nice and hot - there is a fair amount of mass in these connections - I'd suggest 400*C (NOTE THE UNITS IF YOU'RE AMERICAN), but do not hold the iron on the connection for more than about 4 seconds maximum. If you can't fully melt the joint in that time, try pre-heating the board with a hair dryer (not a hot air gun, unless you have one designed for soldering and can set the temperature to about 100*C).
Is this any help? Sorry if this is all basics to you, I never know how much experience people have.
Where in the world are you based? I ask because your profile doesn't say and, well, if you're 5 minutes down the road I'd have a look at it for you.
(As long as you aren't excessively inspired by your profile picture)