All chips installed on the heatsink are linear regulators, so they don't require ultra low esr capacitors or some speciality capacitors, any 105c quality capacitors would do.
You have LM2940-5.0 (fixed 5v max 1A) , a 7815 ( fixed 15v) , a 7905 ( fixed -5v ) , a 7805 (fixed 5v) and a 7915 (fixed -15v) ... so basically you have +/- 5v and +/- 15v and a separate +5v.
All those ICs have input, ground, output ... one pin will be ground, one will be the voltage specified on the regulator (as i wrote above) give or take 0.1v and the other pin will then be input (above the output voltage by at least a 1v). If you measure them with a multimeter and they show fine, no need to replace them.
If you want to use this device, you should use decent capacitors and you should replace even the ones that aren't swollen or showing signs of failure, my guess is the insides overheated and that 4700uF cap is more swollen because it was closer to bridge rectifiers and heatsink...
If you want, I can mail you some quality Panasonic or Nichicon for store price plus a bit for postage, considering i'm in the same country .. should have everything except 4700uF in my personal stock. PM with a list of capacitors you want and I can tell what i have and a price if interested.