Ully: IMO, the best way to "resurrect" a damaged ciruit is replace the compnent/s (I'll do for various pc mobo with capacitors "fatty") or a simple diode blowned on hd's.
The problem (did You already sayd in this post
https://www.dragonslairfans.com/smfor/index.php?topic=1675.0) is the skill for soldering/desoldering.
For training, You can use a secure non working board camed out from a tv or else, and try to solder/desolder components.
On My soldering station, I'll left the temperature around 310/330 °C and, on the desoldering station, around 400 °C (for fast working).
For the tip of the solder, cleaning head is essensial; I use, afther cleaning a uge work, Like Etienne sayd: "take a (small, I add) grinder, or sandpaper and clean the tip".
Afther the treatment I use "firm paste" (I did'n know if the traslation is correct, in Italian is "pasta salda") that make a cleaning/protective treatment on the tip.
Never use water on any circuit, can left umidity,oxide the contact, etc. etc.
To clean a circuit I use acetone or trichlorethylene, with an old toothbrush; never use alcohol!