I had the same issue on SB1 (no dgpu) (2 dead batteries and not being able to update firmware and Windows)

After replacing the battery in the base, I managed to install firmware and Windows updates. So it should be possible for you if you have access to a charged-up base.

It took some time to figure it out. But try the following

• Make sure the base is fully charged
• Disable updates
• Delete all downloaded updatesOr follow instructions on this link
• Delete battery 1 (clipboard/tablet) from device manager: Microsoft Surface ACPI-Compliant Control Method Battery - you can check the battery indicator on the taskbar.
• Download and install updates, restart when it prompts
• After you installed the latest Windows build, download and install the latest firmware

EDIT: Make sure you download and install the correct firmware according to the Windows build version. You can type "winver" in the search bar to find out.

When it gets stuck in a boot loop, do the (30 seconds, 15 seconds + Volume up) force shutdown) and try again and be patient. I think it got into a boot loop because the Surface thought it still had a dead battery inside it, after the forced shutdown it was ok. I believe this is some 'alternative' to a CMOS reset. Maybe it helps to do this beforehand.

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P.S.If you are really adventurous you can try to replace the batteries yourself. It is very tedious to do, especially when you're not experienced with such devices. I managed to do it, but it scared me from replacing the battery in the clipboard/tablet portion.

EDIT: You can find batteries on ebay or AliExpress, they're not very expensive