The 3A line
I just did a test of my own. Using 2 Eveready Gold alkaline AAAs (pretty generic quality) in a crappy 2AAA battery holder (so plenty of extra resistance).
I measured current with the 10A scale of a DMM.
I measured the voltage of the batteries at the ends of the 4" leads attached to the battery holder.
Open circuit (no load) the batteries measured 3.22V
Directly connected to a P4 XR-E, the batteries measured 3.08V, and the XR-E was getting 180ma.
So, with crappy alkaline AAAs, in a crappy battery holder (introducing extra resistance and extra voltage drop at the point the battery voltage was measured), the battery voltage still didn't drop anywhere near what you reported, at over twice the current level that you reported.
There's definitely something wrong with your batteries, connections, or both.