Resolving access and process problems on wordpress site (floridaconstructionnews.com)

The WordPress site Floridaconstructionnews.com is "down" after warnings regarding suspicious processes and excessive resource use. Site is hosted on a dedicated server under our control (with several other domains which are working properly).

See basic description of issue attached. Please note that if you quote a price you should be ready to live with it -- I can answer questions before you start the job but will not accept fake "placeholder" bids.