aa alkalines start out at 1.6-1.7v, level off at 1.5v, and are pretty much depleted at 1.4v.
Most new batteries out of the pack that I've tested come in at 1.55 OCV (Open Cell Voltage). These include AAA, AA, and D Energizer, Rayovac, and Duracell. So 1.55V x 4 = 6.2V = fried ATTiny AVR.
(Energizer Lithium AA/AAA, by the way, is usually 1.8 OCV out of the pack!)
When a cell is "dead' depends on the load you put on it. An alkaline at 1.4 OCV could be put in a clock or remote control and last for months, but try to use it in a bright LED flashlight or with a big motor and it'll fall flat on it's face. As OCV falls, the amount of current the cell can source falls. I find most devices are done with alkalines at about 1.2 OCV, but YMMV.