Holding the buttons together might not be the problem here. If the battery drained and I guess the CMOS did too. It might have reset the BIOS settings. If your laptop has legacy support or UEFI options in the BIOS settings, try enabling them.
In my older laptop, the legacy support would get unchecked/disabled due to which I couldnt boot via the hard drive/SSD. Try enabling or disabling that to make it work.
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