HP Envy 14 Beats Edition Internet Running Slow / Not At All

I recently purchased a new laptop, the HP Envy 14 Beats Edition (i5 processor, 6GB ram) and the internet has been working great (Verizon Fios, MI424WR modem) until yesterday. My internet at that point went incredibly slow all of a sudden, on both firefox and internet explorer. I eventually managed to transfer over some antivirus/spyware/malware software, and found that I had the msiexec.exe trojan, among other trojans (or installers?) on the system. I've deleted what I could find. But, with such slow internet, I couldn't update any of the antivirus software, and eventually did a system restore to out-of-the-box conditions. Using a new internet connection (free wifi at a store), I easily downloaded AVG, Malwarebytes, and Spybot, all of which declared my computer clean. However, upon connecting again to my home internet connection, things ran really slow again.