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The hole on the left circled in green goes to the diode to the right of it. The hole on the right is probably connected on the back side to other switches in the column. Use a multimeter to find which it is connected to and solder to the corresponding spot. Someone with this same pcb could trace out that column for you.
No, it doesn't. The traces for both pins are on the opposite side of the board. The pin he mentioned actually connects to D17, the other diode in the picture. You can see the pulled up trace on the top of the board goes to the little via by that diode. The other pin has a trace which goes downwards, but I can't see under the plate in the pic to see exactly where it goes to. It may be best to scrape the actual trace there and try to solder a wire onto that which is long enough to reach to the switch pin on the other side of the board, but it's a small area to solder to and may prove difficult. Also, the switch will only be held in place by the plate once installed, so that could be an issue when changing keycaps.
Not to be too critical, but in essence the OP has pretty much ruined the board due to (very) poor desoldering technique.
A few tips about soldering:
1. heat the metal contacts with the iron, then add the solder to the joint and iron, then remove the iron once you see the solder has flowed where it should and properly "wet" the contacts.
2. don't leave the iron in place for too long, as this can loosen the copper from the board or damage parts.
3. use alcohol to clean off excess flux after soldering / desoldering.
4. use a good solder sucker when desoldering plated through-hole contacts on double sided boards.
As an interesting side-note, it looks like the
production Pok3r boards DO have full support for LED's, including having the resistors in place, just like the pre-production samples. This is very good news :D