I don't think reinstalling will help in this case,
as in the log, line 10
12/13/2016 10:15:41 AM: This repair was triggered by an exception: #=qzrudOD5UuUNeBdgbHDXhCp3JUuMqdFDUDdntM5Zll9x3DVMYrITWY0RJmzzzktqK: No available GL context found. ---> OpenTK.Graphics.GraphicsContextException: [EGL] Failed to create window surface, error BAD_ALLOC.
Especially on line 04
12/13/2016 10:15:41 AM: Running on Microsoft Windows NT 6.1.7600.0, 2 core
I don't have much information about Windows NT, but I think it's incompatible with latest, and you'll have to use fallback for osu! to run
On very old PCs, only fallback works for them (such as my old PC)
If possible, try enabling compatibility mode
Method 1: Launch Repair Dialog- Hold down the Shift key on your keyboard.
- While holding Shift, double click the osu! icon on your desktop.
- Continue holding Shift until you see the recovery dialog prompt.
- From there, under Renderer, check "Compatibility mode"
Method 3: Config ShortcutIf you don't have the "repair osu!" Shortcut, you can create one instead.
- Right click osu!.exe > Create a shortcut
- Open properties of the shortcut
- Select then Alt + Enter or
- Right click > Properties
- Set Target to ...\osu!.exe -config
- Press OK then open the shortcut
Method 4: Text documentYou can also force the updater to run by creating a new text document in your osu! folder called "help". Right-click in an empty space in your osu! folder, and choose New > Text Document.
Name it help and then run osu! to start the updater in forced maintenance mode.