Will a fresh install help me? (database will not upgrade)

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I'm currently working with a site that's still running 5.4.1.1. I've been attempting to manually upgrade the site incrementally, but the site always breaks once I get to 5.5.0. Upon investigation, it turns out that the core is updating, but the database is not. No matter which upgrade I apply, the database remains at 5.4.1.1.

I have tried to upgrade using the dashboard and I've also tried replacing the core "in-place". Nothing has worked, but thankfully I have backups.

I'm at my wits end. I don't know how to fix this issue. The last thing I can even think of is deleting the site and the database, start with a fresh install of 5.4.1.1, import my database, and try upgrading all over again.

Will this help? Does anyone else have any other suggestions?

CQWeb