You should not have to do #1. No known conflicts with chrome being blocked by a firewall or a antivirus software. The same should hold true for IE, which you can try, but expect the same results(Blocked). This all points to a Malware infection. You probably not going to be able to download the Kaspersky either, possible be blocked by the malware. Now Kaspersky's tool is only for Rootkit(s), other tools will be needed also to check for malware and possibly other rootkit tools
Since your getting these blocks, your going to need another computer(Confirmed clean, NO infections) to download to. You will be saving the downloads, NOT installing, and then copy them to a CD/DVD or a USB device. The transfer to the infected computer to install and run. It's a good idea at first with the first set of scans to have the infected computer disconnected from the internet. After the first set of scans have been done, re-connect to the internet and update the programs installed and then run a complete set of scans again
List of Tools:
Kaspersky(you already know about this one)
Malwarebytes’ Anti-Rootkit
http://blog.malwarebytes.org/news/2012/11/meet-malwarebytes-anti-rootkit/
RogueKiller
http://www.bleepingcomputer.com/download/roguekiller/
aswMBR
http://www.bleepingcomputer.com/download/aswmbr/
AdwCleaner
http://general-changelog-team.fr/en/downloads/viewdownload/20-outils-de-xplode/2-adwcleaner
Malwarebytes' Antimalware
http://downloads.malwarebytes.org/mbam-download.php
HitmanPro
http://www.surfright.nl/en/hitmanpro
SUPERAntiSpyware
http://www.superantispyware.com/
EDIT: You did not have the Extra details posted before I started my answer, that would have been a bit easier if you had. You can probably disregard using the other computer now