Yes your laptop clearly meets the minimum standards for XP, so that is not an issue.
flashing the bios will usually only replace with the default settings, etc, other than removing any custom settings and updates you may have, it does no real harm.
I would suggest trying a win98 boot floppy since that drive works. Use that to load the OS installation from the drive. It still avoids DOS, but it acts as if that step was present. If that doesn't work I came across this:
Simple "ntldr is missing" fix with boot floppy or CD, then fix HD
in my many searches to solve such problems. Perhaps this will help for you as well.