The partition table can exist either in BIOS only, or it can be written to the disk. In your case it seems like it may exist in BIOS only and needs to be written to the disk for the other BIOS to understand it. XBPartitioner can do this but you must use the old BIOS and make sure to write partition table only, don’t format the partitions. There’s a good chance something could go wrong though so I recommend taking a full backup beforehand (either imaging the entire disk or copying over the files via FTP).
It may also be that the partition on disk is wrong and in that case the partition table needs to be removed. The boot into old BIOS (and let it use partition table from BIOS) and write that partition table to disk, then boot new BIOS.
Also, if you write files when the partition table is wrong, it will corrupt the old data, it sounds like this may have happened so I hope you have a backup.