I am a professor at a regional community college, and we have a course designed for exactly the skills you are asking about. We also have a division called Workforce and Community Education. This division's job is to provide credit or non-credit training to businesses and industry in our region. Almost every community college has a similar component. Ours would jump at the opportunity to provide a pre-employment test and/or training for a company like yours, and we (as any other equivalent school) already have the people and resources to do it. If you want to do it in house, you could probably just ask the computer science professor for a copy of their final in the equivalent course and modify it as needed, or hire them for a couple of days as a contractor to make it for you and have it fit your exact needs.
I fully agree that such testing is vital. Before I took this job I worked at a local chemical plant with 3000 employees. Our helpdesk of 10 people spent almost half of their time providing support to the same 7 or 8 employees in the plant. HR would never do anything about it, but there was a huge hidden cost in supporting these people by keeping them on. Also, some regular training on stuff for your current employees will help too, and you'd be surprised at how little it might cost doing it the way I've outlined. Good luck.