I'm pretty sure I don't have any malware left on my PC
Your logs show that there are some Windows Defender processes running but no Windows Defender service so I wanted to make certain that there is no active malware involved.
I can suggest a few options you can try for restoring the Defender service:
I strongly recommend that you back up any important files and folders before you continue.
1. Uninstall then re-install SP1
2. Do a repair installation of Win 7 (that is also known as a non-destructive installation - it should not affect your programs and files but you should still back up your files first!)
3. Install Microsoft Security Essentials - MSE includes defender and you do not presently have any antivirus program installed.
We could try to restore the service, but that is more complicated and it makes more sense to try one of the above options first.
If anyone else has another suggestion for how to proceed, please do chime in.