palemoon-27.6.0a1.win32-git-20170929-bc251e93-xpmod.7z is the oldest New Moon 27 version at https://o.rths.cf/palemoon/. Roytam keeps every version on his website, but that one probably has several bugs.
Unless you have a specific reason for running an old version, you'll probably have better luck running the current version of NM 27. Try one of these instead:
palemoon-27.9.6.win32-git-20190615-b33dced90-xpmod-ia32.7z
palemoon-27.9.6.win32-git-20190615-b33dced90-xpmod-sse.7z
palemoon-27.9.6.win32-git-20190615-b33dced90-xpmod.7z
Try #3 first; if it doesn't run, try #2; if it doesn't run either try #1.
#3 is for newer CPUs; #2 and #1 are for successively older CPUs.