Cannot open Downloads folder. Get the following pop-up message: "The operation can’t be completed because the original item for “Downloads” can’t be found."

It sounds like you're trying to open the Downloads folder via an alias. Go to your Home folder and make another alias for the Downloads folder and put the alias wherever the current alias is located.

If that's not the situation post back with a screenshot of your Home folder contents and detailed description of your situation.

What Old Toad said.

Also, in case you are keyboard oriented: there is a shortcut to reach the Downloads folder directly:

Command-Option-L