Cleaning sugary drink from a board

[SeanB]

First remove the chip, and then clean the board under it. Then gently remove the solder mask both top and bottom ( and in this case likely the tracks as well) to bare copper, flux lightly with liquid flux, and use a strand of tinned copper wire through the hole soldered top and bottom to remake the via. then clean the board again and apply a protective coat of clear varnish ( clear nail varnish is good for this, as it is not readily visible, and it is not really available in PCB green) to protect. Then solder in an IC socket and replace the chip after cleaning the board again with IPA. Take the pins on the IC and straighten them and use solder wick to remove excess solder.

[Shock]

Looks like someone has reflowed a few pins already. It's hard to see from the picture but if you believe those two tracks are ok and the via to the pins are also ok.  I would add flux on top and underneath and then reflow the pins with a touch of leaded solder with your iron from the underside. Then clean and retest the board. Just don't over work that area too much that's all.

On these old boards reflowing them is sometimes needed to get the chip out easily as well.
If you cannot get good wetting to the top of the eyelets it means they are too corroded (or your didn't clean enough).
A proper clean and inspect will require the chip out and you will always want to socket it as SeanB mentioned.
I personally don't remove things until I've ruled out bad joints.

Additionally if you haven't removed solder mask off a via or track before or soldered to one this is a challenge in itself.
As it's delicate work I would practice on an old board first.

Watch the complete series of the Pace repair and rework videos they are excellent.  They cover the important techniques of cleaning, flux and tinning. https://www.youtube.com/user/paceworldwide