I attempted to install on Windows Server 2008 R2 Service Pack 1 and had the same problems.  I thought it might be proxy since I'm behind a firewall, but setting the usual values did not allow the program to overcome whatever it is that PIP is having problems with.

here's the log at the failure point:
MSI (s) (2C:BC) [11:10:26:806]: Executing op: CacheSizeFlush(,)
MSI (s) (2C:BC) [11:10:26:806]: Executing op: ActionStart(Name=UpdatePip,,)
Action 11:10:26: UpdatePip. 
MSI (s) (2C:BC) [11:10:26:809]: Executing op: CustomActionSchedule(Action=UpdatePip,ActionType=3090,Source=C:\Python27\python.exe,Target=-m ensurepip -U --default-pip,)
MSI (s) (2C:BC) [11:10:26:812]: Note: 1: 1721 2: UpdatePip 3: C:\Python27\python.exe 4: -m ensurepip -U --default-pip 
MSI (s) (2C:BC) [11:10:26:812]: Note: 1: 2262 2: Error 3: -2147287038 
Error 1721. There is a problem with this Windows Installer package. A program required for this install to complete could not be run. Contact your support personnel or package vendor. Action: UpdatePip, location: C:\Python27\python.exe, command: -m ensurepip -U --default-pip 
MSI (s) (2C:BC) [11:10:30:520]: Note: 1: 2262 2: Error 3: -2147287038 
MSI (s) (2C:BC) [11:10:30:520]: Product: Python 2.7.10 (64-bit) -- Error 1721. There is a problem with this Windows Installer package. A program required for this install to complete could not be run. Contact your support personnel or package vendor. Action: UpdatePip, location: C:\Python27\python.exe, command: -m ensurepip -U --default-pip 

Action ended 11:10:30: InstallFinalize. Return value 3.

To get this to install, during the installation, disengage entirely PIP, it's default is to install it.