Try a direct link and download to install. Scroll down to find the latest release and the correct language version and then download and install.

https://archive.mozilla.org/pub/firefox/releases/

If that old HP laptop is using the eol Windows 7, 8, 8.1 then the most current you can run is Firefox 115 ESR. It is currently at 115.17.0esr and will be supported up til at least 115.21.0esr in March 2025. Fx 116.0 and later requires Windows 10/11 to run.

https://archive.mozilla.org/pub/firefox/releases/115.17.0esr/ https://archive.mozilla.org/pub/firefox/releases/115.17.0esr/win32/ https://archive.mozilla.org/pub/firefox/releases/115.17.0esr/win64/

However if you have Windows 10 or 11 then you can run the current Firefox 132.0.2 or Firefox 128.4.0esr from https://www.mozilla.org/firefox/all/

Also you can download the full offline setup Firefox .exe and then transfer over to the old laptop with a usb flash drive to then install the newer version.

Since you have such a old version of Firefox perhaps you should backup your Profile(s) just in case before installing the new version of Firefox. https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles

I only have the XP which needs a Win 32 installation. The one you recommended is a 64 bit.

Strangely enough, when in the Firefox browser, it states that the current installed version (41.0.1) is the most current up to-date version. Perhaps that is the last version that will work on a Win 32 bit o/s.

I only have the XP which needs a Win 32 installation. The one you recommended is a 64 bit. Strangely enough, when in the Firefox browser, it states that the current installed version (41.0.1) is the most current up to-date version. Perhaps that is the last version that will work on a Win 32 bit o/s.

The old Firefox 52.9.0esr was the last version to still support the then eol WinXP and Vista at the time. The Win64 version of Firefox required Windows 7 or later at then time as WinXP/Vista was only supported by 32-bit version even if you had 64-bit WinXP or Vista.

https://archive.mozilla.org/pub/firefox/releases/52.9.0esr/win32/ https://archive.mozilla.org/pub/firefox/releases/52.9.0esr/win32/en-US/ https://archive.mozilla.org/pub/firefox/releases/52.9.0esr/win32/en-GB/

https://support.mozilla.org/en-US/kb/end-support-windows-xp-and-vista

Honestly you may be safer going online if you try and get a current 32-bit (or 64-bit if CPU is 64-bit) Linux distro with a lighter desktop like say XFCE or Mate as avoid heavier ones like KDE or Gnome. You can dual boot or replace the WinXP install. Downside is there are not many supported 32-bit Linux distros now days. However this way you can use more current and secure Firefox versions.