One of my Ryobi 18v battery packs (1400672) won't charge, the chargers red and yellow lights stay on. How can I trick it into charging?

Use
AC / DC Power Adapter Replaces Ryobi One+ Batteryhttp://lcdpayless.com/ryobi_one_power_adapter.php

Since your battery is most likely a NiCd battery, one or more of the individual cells inside the plastic case could be defective. Do what I have done and replace those NiCd batteries with Lithium batteries. They last much longer and can be left charged for a year without being re-charged, ready for when you need a drill or whatever tool.
Do NOT charge a Lithium battery in a charger designed for those NiCd batteries. The tech who replaced a set of Lithium batteries for me told me that will kill them. However, a green charger will charge both NiCd and Lithium batteries. The green charger will charge a battery in about one hour.
The idea of converting a cordless tool to a corded tool is ridiculous. Why do we buy a cordless tool? To use it where we don't have to worry about running an extension cord.

You can't! there's a overheat overload inside the battery pack.