There are a lot of different things that cause computers to slow down. Among them like everyone knows are viruses, malware, and adware. Another is all of the overhead that gets loaded into the registry and in the start up sequence that never gets cleaned out even by the most reputable of software.
To really get a computer as clean as you can without reinstalling Windows from scratch try the following first...
Autoruns Autoruns for Windows
This one is a little tricky as you have access to everything that loads and runs in the background. A lot of it most people will have no idea whether it is something to leave a lone or to get rid of. It does have a convenient right click context that allows you to do a google lookup of everything. Disabling the things that are no longer installed or that are not needed will definitely speed up not just the start up process but regular running conditions as well.
Viruses and More:
Reboot your computer into safe mode with networking
Get a couple rootkit detectors and cleaners, I recommend rkill Downloading RKill
and tdsskiller TDSSKiller Download
Use Vipre Rescue VIPRE Rescue - VIPRE Computer Recovery Solution
This is a rescue scanner that will scan in windows. You may be confident in your antivirus but believe me there is nothing out there that catches 100% of the thins 100% of the time.
Eset Online Scanner: Free Virus Scan | Online Virus Scanner from ESET
Another scanner to be able to double check antivirus effectiveness, no matter what you use this is a necessity to do.
Next of course is to check for malware and adware. Believe it or not most antivirus programs are not as proficient at this as a couple of the programs specifically designed for it. Of course there is the industry standard Malwarebytes Malwarebytes : Free anti-malware download
and the second is Emsisoft's Antimalware Emsisoft Anti-Malware for best protection - Free removal of Viruses, Bots, Spyware, Keyloggers, Trojans and Rootkits
just like malwarebytes comes with a paid and free version...once you have run these two and cleaned whatever they have found run JRT (Junk Removal Tool) Junkware Removal Tool Download
Under most circumstances this will have the computer pretty clean if not totally depending on how much was actually in it, if it is to messed up I would definitely recommend a professional, sorry but that is just the case.
What most people forget is the removal of add-ons and any proxies in their browsers, not just one of them but all of them that are installed. You can do this manually like I usually do or you can download and use Avast's Browser Cleaner that does a pretty good job at http://files.avast.com/files/tools/a...er-cleanup.exe
Once this is all done then rebooting your computer into regular mode and doing the standard maintenance like sfc /scannow running chkdsk, and a few other standard things are going to have you cleaned up and working about as well as it is going to, that is unless say things like sfc come up with errors that it can't fix and then it gets a bit more complicated.
You did good in your cleaning you just forgot a couple of steps that could be making a world of difference