I've had similar experiences. My most recent I've walked into an already running db/website. They had an audit history table that had built to about 80M rows and was replicated up and down into four other databases. It took about four hours to go day by day to move everything into a history table and delete older than 60 days from the current table. We saw about a 20% increase on the front end.

Then the DB served multiple unrelated facilities/companies. The SP to look for authorized employees didn't have a facility qualifier on it. So it was looking through a list of over 40K current and former employees from every company that ever used it. We were working on correcting it when we were bought out.

The free SQL monitoring tools helped spot some of this.

But I thoroughly agree that you need to look the current before you just go for hardware.