Trojan Alureon.A Detected After Clean Win7 Install

A brief intro: I'm working on a family friend's laptop. It's a Dell Vostro 3550. After doing a factory reset, I was still getting tons of BSODs. You can find info on all that in this thread. I did a Clean Windows 7 install because all signs pointed to hardware issues, but we wanted to be sure.

The only things I put on the laptop were a WiFi driver, Windows Updates, and MSE. MSE immediately detected Trojan Alureon.A. I had it do what it could, then it suggested using Window Defender to finish up removal. Before I did that, I did some googling. I installed MalwareBytes Anti-Malware, which detected nothing. I then got Kapersky's TDSSKiller.exe, which detected the rootkit and seems to have successfully removed it. I rescanned with all tools after reboot. MSE showed that it had detected, but successfully quarantined tons of variants containing "Trojan Alureon" in their name, but different letters at the end. I had it remove them, which it did. I've rebooted several times, run scans with all programs multiple times, and all seems clear. I wanted to make sure I was out of the woods before I continued gradually installing drivers and programs. Someone in my thread told me to come and post here.

Thanks so much for replying, Borg!

If the virus did hitch on to something, it was probably the HD. I downloaded the installer for Win7 from my personal laptop, as well as the WiFi driver I mentioned. I have not returned the documents/files to the laptop, yet. When I was reinstalling, I noticed there were 3 partitions: Boot, Recovery, and OS. Will the HD wipe format/clean all three? I know that's probably a stupid question, but I wanted to make sure I completely understood everything.

Okay, thanks! I am running the autonuke options per the directions.

Yes, from what I understand that's the best way to make sure the virus isn't hiding somewhere on the HD. I will just need to do another clean install afterwards. Is that correct?

Flash drive, like the usb drive? I have a 1 TB external hard drive, which I back stuff up on. I used a DVD to reinstall Windows 7. But, I did download the wifi driver via my own laptop and put it on the usb drive to transfer to the problem laptop. I'll scan it for viruses/malware to double-check.