Fix Joomla, Joomdle and Moodle after hack

Our site was hacked with code from another site that injected code into a bunch of files. The bad script was taken care of and the injected code has been removed, but there are still issues with our site. On Joomla site will not allow anyone to sign on. It redirects back to home page when you try to log in. On the Moodle site, the same thing happens. As the bad script started, Joomdle would not connect the joomla and moodle sites. That also needs to be fixed. I can log into the back end of Joomla. The version is 2.5.9. I tried to reinstall the 2.5.9 update and it did not fix the issue. My host suggested that I replace the core files, I will leave that up to you. You must preserve all data and site formatting. Also, some of the graphics do not show up. Please be able to communicate well in English. Please do not bid if you are going to ask me to release milestones before the job is done. I have been down that road before and have lost money.