Please help...TS3 says I need to reinstall Base game :/

I'm not sure why your install stopped working all of a sudden. But one possibility that comes to mind is that your thumb drive has a different letter now than it did before. You can check the letter assigned to it in a File Explorer window. If it has changed, you can try manually reassigning it, or plugging in your external drives in the order that would give this thumb drive the correct letter. Drives are usually (but not always) lettered sequentially as they're read by the system.