WordPress Repair: Plugins, PHP Update

My WordPress site suddenly dropped its side-widgets, the layout broke, and I now run into the infamous white screen of death whenever I try to activate roughly a dozen plugins. Some of those plugins are non-negotiable because the theme depends on them, so I can’t simply wipe the slate clean... (Budget: $250 - $750 USD, Jobs: CSS, HTML, PHP, Web Design, Web Development, Website Optimization, WordPress, WordPress Plugin)