Here is a good list of tools you can use to troubleshoot/fix Windows. Though not a complete list it is a good start. Please feel free to add on to the list if you know of anything worth using.
I tried to include only portable versions of the programs so you can keep them on USB keys.
Avast Portable (http://www.pendriveapps.com/avast-virus-cleaner-virus-and-worm-removal-tool/)
AVG Portable (http://www.pendriveapps.com/avg-anti-virus-rescue-usb/)
SuperAntiSpyware Portable (http://www.superantispyware.com/portablescanner.html)
Spybot Search and Destroy Portable (http://portableapps.com/apps/security/spybot_portable)
Hardware Testing Software
Seatools for Windows (http://www.seagate.com/support/downloads/seatools/) – Hard Drive testing including SMART status for internal drives
FurMark (http://www.ozone3d.net/benchmarks/fur/) – Stress test graphics cards
Prime95 (http://www.sevenforums.com/tutorials/100352-hardware-stress-test-prime95.html) – Stress test CPU (includes instructions)
Memtest86+ (http://www.memtest.org/) – Memory test (I recommend the USB version. Installer in the downloads. Requires Windows to setup)
Combination Live-CDs (more advanced tools generally)
Ubuntu-MRT (Malware Removal Toolkit) (http://sourceforge.net/projects/ubuntu-mrt/)
Ultimate Boot CD (http://www.ultimatebootcd.com/) – Crazy amount of tools. Well worth using if you spend some time to learn.
Ultimate Boot CD for Windows (http://www.ubcd4win.com/) – Similar to UBC but with some added Windows specific tools