In case anyone finds this while searching on the same issue, what I did was pull on the battery (in the direction of removal) while pushing down on the edge of the laptop (near the battery latch) that was sitting above (bulging above) the battery using a screwdriver. The bulging lip snapped back below the battery, at which point it was easy to fully insert the battery and then release the latch to remove the battery.
I guess this ebay seller goes through so many laptops that he/she just slaps the battery in without looking to see if it's properly inserted.
T430: i5-3320M(2.6GHz), 8GB RAM, 120GB SSD, 14" 1600x900, NVIDIA NVS 5400M 1GB
W510: i7-720QM(1.6GHz), 8GB RAM, 240GB SSD, 15.6" 1600x900, 1GB nVIDIA Quadro FX 880M
T410s: Core i5 2.53GHz, 8GB RAM, 120GB SSD, 14.1" 1440x900