I uninstalled a (working) 4.3.15 test build and installed the 4.3.16 release. Several problems:
1. The VirtualBox UI was not working right after install. There were no error dialogues; the process just went out to lunch and nothing happened. I then tried to reboot the computer, but...
2. ...I got stuck on the Windows "Shutdown" screen with the spinning widget for quite a long time, so I ended up hard power-cycling the PC.
3. On next startup I again tried to start the VBox UI and got the following error:

Afterwards I noticed that...
4 ...All other apps on my PC stopped working. I could not launch my browser. I could not kill the VirtualBox process in TaskManager. I could not shutdown or reboot the computer which became very unstable. Eventually I started getting error messages from Windows telling me to hard power-off the machine.
5. On next startup I tried to uninstall VirtualBox but the uninstaller is not available! There is no VirtualBox entry in "Programs and Features" in the Control Panel. There is also no uninstaller link in the VirtualBox menu:

At this point I am unable to uninstall the app which is causing major stability problems on my desktop and would appreciate your help/advice.
I am not able to provide a useful log because the only ones available on my filesystem are older logs from previous installations (they predate the installation date of 4.3.16 which is 9/10/2014). It appears that a VBoxStartup log was not created since I installed 4.3.16:

My configuration is:
Windows 7 Pro SP1, 64-bit
Avast! Internet Security (subscription version, not free) program version 2014.9.0.2021