Dealt with AL.E3 on MR-J4 more times than I want to admit. The battery thing is obvious but here is what people miss: if the battery went dead during a long shutdown, the multi-turn counter has lost its absolute reference. Clearing the alarm and jogging to TDC is only half the fix.
What I do after battery replacement: 1) Clear AL.E3 with alarm reset. 2) Switch to JOG mode, NOT auto. 3) Jog to TDC using the handwheel at the slowest increment — I use 0.001mm steps for the last 5mm. 4) Verify TDC mechanically with a dial indicator on the slide, not just the display. The display is meaningless until you re-establish the reference. 5) Write home position via PA03. 6) Power cycle and verify the absolute position holds.
The part that bit us once: we jogged to what we thought was TDC based on the old position display, wrote PA03, and ran a test stroke. Turned out we were 0.15mm off because the encoder had drifted during the power loss. The die hit the shut block. Now we always verify mechanically before writing the home position. Takes an extra 10 minutes but saves you from a very expensive mistake.
Also — keep spare MR-J4 batteries in the cabinet. ER6V lithium, about $8 each. Replace them every 2 years whether they need it or not. Way cheaper than a recovery procedure.