If you did this test properly and the column 4 lamps lit when they were supposed to, you can stop looking at the boards. I love this lamp matrix tester, but the jumpered test can get you the same results with a bit more work.
http://www.siegecraft.us/presta/index.php?id_product=11&controller=product&id_lang=1

The most likely cause of a column not lighting is a broken wire. For columns, you can test DC voltage, and you will normally see something close to 3V (due to the 18V being pulsed). Test it at the connector to start, then test again at the lamp board. From there you can narrow down where the open would be.

If you do desolder it, I would recommend replacing it with a socket and a new chip.

A logic probe is cheap, and if it saves you having to remove a single IC, the time saved has nearly paid for the probe. I didn't shop around, this is just the first one that popped up:
https://www.amazon.com/Elenco-Electronics-LP-560-Logic-Probe/dp/B000Z9HAP4