My apologies for the delay in getting back to you.
With the issue affecting 3 different devices that are trying to print to the printer. This tells me a few things.
The issue is wireless related, either to the printers wireless connection or settings, or the routers.
So lets try the following, try unplugging the wireless router, and the printer from power for 1 minute. Actually unplug them from the socket. Then plug them back in and test.
if you dont see the printer printing in the first 30 seconds.. Then move to the next step.
Reset the printers network settings, heres how http://support.brother.com/g/b/faqend.aspx?c=us&lang=en&prod=mfcj6710dw_all&ftype3=2041&faqid=faq00000105_015
Once reset, reconnect the printer to the wireless network. On the printers control panel go to network, wlan, setup wizard. Reconnect the printer to the wireless network.
Once its reconnected, attempt to print.. Any change in the time or printing behavior?
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Senior Technician and Network Switching Systems Operator / Maintainer.