The processor reports in that dmesg the keyword "LONG" which indicates 64-bit support. Plus it reports it is a "Core 2 Duo," which is a major brand of 64-bit capable processors from Intel. That particular model of processor was launched in 2009, the same year as your BIOS. There may be more recent BIOS versions available from HP.
I can only conjecture for the reason Debian may have failed to boot, but it is possible that the boot failure could have been BIOS related.
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