The most common error with defrag is a disc that has less than 15% free space. Did you get an error message? Is your disc vey full? My computer>Local disc C>Rt. click>Properties.
Congratulations on your backup! You are well ahead of the curve on that. It is possible that there is, in fact, no password, and that simply clicking OK, or Continue/next would get you in to Repair. Is it a Repair installation that you attempted, or were you trying to use the Recovery console? From what you have described, I'm not sure you need to "Repair" anything anyway.
Many folks think that the problems they are experiencing are more serious than they turn out to be. Why not post back with as many details about your system--both hardware and software as you can, and include as many specific details about your experience of "slowness" as you can remember. Please do not post a HiJackThis log in this section of the forum.
As far as your 2478 Registry "Problems" go, please bear in mind that the overwhelming majority of these "problems/errors" are simply invalid entries which no longer function. I admit that that seems a high number, but just removing the invalid entries will not "fix" anything except free up a little space. When there are real Registry problems it is because of an improperly configured, but valid entry that is causing improper function. That requires Registry "editing," something for which almost all of us require experienced help. Such help is available if and when it is determined that it is required, but for now I suggest you relax about the Registy, post back with more details, and the Geeks to Go staff and members will help you get your system back to normal.