Theme problem: Slow Admin (Logged in), Fast Front (Logged out)

I have a site where only the admin part of the site is impossibly slow (~4 minutes per page). I have tracked this down to the theme that I am running which the creators’ say they no longer support. That being the case, I don’t think anyone here is likely to have the exact answer to the issue, but I am looking for debugging suggestions or “gotchas” that I may not know about. (I am versed in PHP but at the low end of knowledge when it comes to WP.)

Thanks!