The newish 3500mAH batteries die pretty easy. I had 4 of them in my TMo4vn (which has a constant, blue LED power available light) and have killed 3 of them dead dead dead. These are the first batteries I have ever run across that simply die from overdischarging.... They were NEW too, so I'm not very impressed with them.
Are you sure they weren't protected 3500s. . If the protection trips it will read 0V. A good smart charger will not charge it. So, jump it or buy a Cheap not so smart charger that will pump anything.
Also, Panasonic 3400s are made to go to 2.5V, while other brands are 3V. On a single cell or parallel amc7135 based controller lights it is impossible to go much below 2.9 volts, as the FWV at 300 is 2.7 and the controller dies at just below .2V above FWV.
About the only time one can safely take advantage of the extra runtime is in a buck controller, like the buckpuck, with a 2.5 v cut off and 2plus cells in series. You might get much significant time in a 4s18650, or small significant in a 2s. If your electric socks or work light or bike light dies, even half hour or hour shy of full daily service time, over 300 days a year, it means double cycles, plus, upwards and into, thousands of dollars lost, from a business point of view. . So, 45 minutes of lost runtime, is a big deal. . Even for recreational usage, multiply number of users of your product times how much inconvenience time. .