Your best bet is probably to "hot-plug" the drive, either directly into its SATA connector or by using an ATA-to-USB cable. That way you can boot the OS and then let it
deal with the drive, without letting the firmware get involved.
As to your bigger question, the firmware shouldn't
care what's on the disk, but in practice they sometimes do. To the best of my knowledge, no firmware can understand NTFS, so if that's what you're using, it's unlikely that it being full was what caused problems. Some firmwares, though, do try to interpret the partition table and/or the contents of FAT filesystems. This can result in bugs such as what you're seeing. I ran into something that could cause a Gigabyte motherboard with "hybrid EFI" to flake out in a way that similar to what you describe; you can read about it here.
It's unlikely that the underlying cause is the same, but it's conceivable it is.