I assume you are booted into a Linux distribution running on your hard drive, correct?
Gparted or DISKS should allow you to format the drive to GPT. And choose an EXT4 partition. You say you want EXFAT, is there something wrong with EXT4? Is EXFAT only one greyed out like you said, but other partition options are not greyed out? Agian, I'd try EXT4.
If you can't format or choose other partitions, then the drive might be toast.
Again, this is all assuming you are NOT booted off of the USB drive that you are trying to format. This is all assuming you are booted off of your HARD DRIVE.
I say this because, you can't format a drive your booted off of.
StarTreker

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