Firstly try the quick way to install grub.
Boot from the live cd/usb and select try ubuntu.
When the desktop loads open up a terminal and enter
sudo mount /dev/sda4 /mnt
If that completes ok reboot and take the cd/usb out.
sudo grub-install --root-directory=/mnt /dev/sda
All the above should be copy/pasted into the terminal window as this will stop typing errors.
The system should now boot into your Ubuntu installation. If it does open up a terminal and run and watch to make sure that the Windows menu entries are picked up. If they are please reboot and try to boot Windows from the grub menu.
If that works everything is ok. If not get back to us.