I have installed the SUPEE 8788 patch without using SSH. I am using following link
Now the admin panel is blank after login. And can't place orders in frontend
Make sure to clear cache from backend by going to file manager to /var/cache folder. Then refresh browser. Had exactly same issue.
If this doesnt work. Revert the patch, and make sure complier is DISABLED!. Then install the patch one more time.
Please turn on error reporting and enable developer mode. Then again check admin panel. If you see error message there, then you can further debug for this issue and fix it.