Problems with Mozilla opening most pages

Hi! Since I downloaded a driver for a mouse from one Russian site, I've ran into serious trouble. The download from this cursed site filled my computer with all kinds of adware, spyware, slaveware, malware, trashware, bullshitware, bitcoin miners, Trojan horses, browsers and everything hijackers and other dangerous viruses. First I've got a very offensive advertisement on Mandarin (traditional Chinese)appearing on the lower right corner of the screen. I uninstalled ''MTV'' which appeared to be the ads sender but the most problems are still unresolved. In my browser, Mozilla and the alternative one, Internet Explorer the main pages of both browsers were replaced with ''feed.snapdo'' once and lately with ''http://search.safefinder.com/?st=sc&q='' these are ''search engines'' with interface m
 ade to immitate that of Google but they don't show real results, they show only advertisements and sponsored links. I learned from this by downloading SpyHunter, it scanned my computer and i
 t found a Total of about 250 threats, some of them with high level of danger. I didn't want to give dozens of dollars for this and then I turned to alternative solutions: AVG, Microsoft Security Essentials, AdwCleaner and used my installed from before CCleaner, I also tried from coltrol panel and thoroughly checking all the folders from local disks C and D and whatever other folders I could find. The results of these programs were a little more than nothing, but the main issue I'm turning to You for help is that I can't use my favourite browser Mozilla. Aside of the annoying fake search engine(which replaced the very convenient Mozilla main page which contains the button for previous session tabs open again), Mozilla can't open any pages but the ones from bigger sites - of the amount of p
 ages I tried, only Google, Google associated sited like Gmail, Youtube, etc. and some other sites like Kaldata (local, Bulgarian site). No other sites can open, even when I click some of the
  links that Google gives after I search. The sites (the very vast majority) that don't work, when clicked on them I get the ''problem with connecting to the page'' tab and the usual options listed. I uninstalled Mozilla and installed it again, my bookmarks were saved, the annoying search engine disappeared, but the main problem is still around I tried also changing the proxy server settings from the options menu but still no result. Please help, The download I made was on 19 January and now i've got a few days in which I use IE but it's uncomfortable for me. Help with ideas and also some good way or software to clean my computer from the viruses and, of course, to fix Mozilla.
And one tip: NEVER, NEVER download ANYTHING from these cursed Russian sites, you can run into this trouble too.