I hired someone to fix the problem and this was their diagnoses:
The theme you are using has hard-coded calls to plugins inside of it (now it's fixed and it checks if the functions are available before calling them). When you updated your PHP version, some plugins didn't function properly, so you had to disable them which broke up the theme you are using.
Also the theme is using deprecated functions of WordPress and you will probably have to change it (the theme) soon. For the moment, these functions are still supported by WordPress/PHP but in the future they may drop support for these functions.
I would recommend not updating WordPress or PHP by yourself for the moment. The problem with not updating is security vulnerabilities. Two major vulnerabilities have been found in WordPress' plugins like W3 Total Cache last week and in this case, an update is mandatory.
Check this link for more info : http://www.acunetix.com/blog/web-security-zone/wp-plugins-remote-code-execution/