Finding dead electric wire underground
If I were you, I'd just plan to make a new trench and run new wire. Here's why


It sounds like a previous DIY project, which likely means it wasn't done correctly. Common problems with this are they used NM wire instead of UF, and they didn't bury it deep enough (needs to be at least 12" by code)
The previous wire might not work. If they used NM, there's a good chance it's got some damage by now. Even if not, the ends might be damaged after being buried exposed, and trying to splice in an outdoor setting is a pain. Just avoid the problems and run new wire.
Add conduit. It's cheap, it better protects the wire, and it's neater.