My first recommendation is to calculate your cost of downtime due to a failed hardware or software component you control. In some manufacturing environments even an extra hour (if your out of the office and need to drive in) could pay a $25k salary for a year.
Next is to focus on getting a dedicated resource for intake of calls/emails and to handle most of the running around. The first 2 years someone is out of school they are most willing to work for really cheap. Introduce yourself to some teachers at the local community college or trade schools and even see about getting some students during their on the job training to show the improved response time to incoming requests without actually costing the company money.
Once management gets better service, losing it might just make them more willing to pay to get it back.