Elitebook 540 G3 not booting up

[BrewGuy]

Elitebook G3 not starting up (note: product says is G3, but when I entered the serial number on the site it came up as G5).

When I start up the laptop, the power button lights up (and there appears to be a very quick light on the screen but hard to say), and then flashes regularly with about 5 seconds gap (this does not appear to match the blink codes I have seen). This happens regardless of whether the laptop is using battery or mains power. This has happened for a few weeks now - on occasion the laptop would start and work OK, but it has failed to start at all when tried. 

Here are the actions I've taken:

1) When it did start I ran a diagnostic test and it said there was an issue with the battery

2) For a while, if it didn't start and I removed the battery and replaced it, it would then start. This does not appear to work any longer. I also reset the laptop once just in case this helped. Since then, nothing has worked, including the following:

3) I have tried removing the battery and holding down the power key to remove any static in the system. This does not appear to work

4) I have tried restarting the laptop and pressing various F buttons to try to access the start-up menu. This does not work and I cannot access the start-up menu

5) I've tried disconnecting and reconnecting the CMOS battery in case this helps. This did not appear to work

The issue started happening without any apparent issues at my end (didn't spill anything on it, drop it, or anything similar, nor made any weird changes before the issue starting).

Thanks in advance for any help.

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