I would expect to hear this problem with PC's, but it's odd that it should cause your A4000 not to boot…
With or without the battery I presume that A4000's should have no problem (As many users have Amiga's both with and without any internal clock battery), so all I can presume is that the voltage on the battery is at a crucial level, where, by some means, it’s causing unpredictable switching in the RTC and corrupting data on the bus. But that's just my guess.
Just to reiterate: Swap, or at least remove the original battery if it's still fitted!
PS. I’ve always assumed that, in PC’s fitted with the 3v lithium cell, that a few hundred microampere float current is present when the machine is powered up just to help extend the life of the cell, even though they’re not meant to be recharged.
Is this true? (Though, without any charging system it’s a terrific way to make sure that the system *dies* after a couple of years and needs replacing…Unless you know to swap the cell…)
Hodgkinson.