I'd like to thank everyone who contributed to this discussion, as it led me to a couple of ideas that I used when testing the charging method for this laptop. I am marking this solved only because I was able to get the battery to charge to 100% again... HOWEVER, I was unable to get the the root of the problem, and I doubt that this fix will work on other laptops. What I discovered regarding the trickle charge (thanks mateo and neon_overload) was that the energy provided during the time that the computer was on was ineffective in charging the battery, presumably because too much power was being provided to the system. When the battery is above 90% charge, there seems to be a safety mechanism built in that keeps the battery from charging too much, and it was being activated any time I tried to charge the laptop from above the measured 90%. To fix this, I drained the battery to 80% (of the measured capacity, not design capacity), and pulled the battery while the system was on. I then powered the system down and plugged the battery back in. This made the system avoid trickle charging and also avoid the safety mechanism that is built in. 20 minutes later the orange flashing light that I had been seeing disappeared, and the white charging light turned off, indicating that the battery had charged fully.

Thanks again for all of your help guys, it's much appreciated.

linux_RRT