The most possible causes of the issue Toshiba external hard drive not showing its full capacity are a wrong partition table and the caddy of the external hard drive.
Based on your description "I actually put a different HD into the Toshiba caddy and that didn't work either so the connections on the Toshiba are faulty," the first thing you can try is to get a decent caddy/enclosure for the external drive, then connect it to your computer again.
If the problem remains, then it could be a wrong partition. Disk volume space larger than 2TB is known to be unsupported by the MBR (Master Boot Record) partition table. Owners of 3TB and 4TB hard drives may therefore find that there is less hard drive space than is ideal. You must convert MBR to GPT (GUID Partition Table) in order to address this kind of issue.
If you find some data loss when the external hard drive shows its full capacity, you can try data recovery software such as iBoysoft Data Recovery for Mac to quickly recover lost/deleted files. You'd better not add new files to overwrite the data before the recovery.