Lots. For starters, check to see if the machine's overloaded. If the apps are running slow due to lack of resources, that would make network performance appear slow. Check the message logs for possible problems. Try pinging things and see what sort of response times you're getting.
If possible, isolate the affected machines onto their own private network just to make sure that traffic or errors from outside sources isn't polluting your throughput. Look at the stats in ifconfig.
Look at the stats logged by your routers. If possible, get a network analyzer tool. They're not cheap, but neither is your time, most likely.
There are undoubtedly other things that could I could come up with. These are just items off the top of my head and without having firsthand knowledge of what's going on your network.
Customer surveys are for companies who didn't pay proper attention to begin with.