SpaceFlight.com can handle the launch. Why do you want a LEO orbit, there might be better orbits for your mission? You'll probably want a radhard processor instead of a Pi Zero. You will also need Batteries, Thermal, Attitude Determination and Control, RF and antennas...minimum budget is probably $1M including launch for a "server in space" mission. There is a lot that goes into making a spacecraft. A good book to pick up is SMAD[0]. Reach out to me if you have the resources, I'd be happy to help.
[0]https://www.amazon.com/Space-Mission-Engineering-Technology-...