The boot info summary tells us that you've got a fairly standard system. Unfortunately, the information is already outdated as you attempted to install Ubuntu on sdb.
There's something weird about your screenshots. You've got mbr partitioned hard drives and you old system in installed in legacy mode, but your new install on sdb created an EFI partition, suggesting you installed in UEFI mode. Best not to mix modes.
You can use a dirty reinstall. You can use manual partitioning ("Something else"), select sda1 to use as root partition and NOT format it. That will reinstall Ubuntu, leaving your documents untouched. It's more convenient though to have your documents and the OS in separate partitions.
But I think right now it's best to use a clean install, as TheFu suggests. Copy your documents to a backup drive, disconnect the backup drive, install, restore your backups. If you wish, you can take the opportinuty to repartition your drive.
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