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So, a slow network connection is normally caused by the network devices FIRST.
Then, it could be the connection itself......possibly cabling, or being on the "last mile" of the network node of the internet provider.
Can you run a internet speed test please, and report here the results (take a screen shot, and upload here)
You can use the link below to do the test.
So, if multiple computers suffer the SAME problems in the network space.......it could very easily be a network device. Such as a switch, router, Access Point, Modem, etc etc.
What is your Internet provider?
I assume you have taken the MBPro to OTHER areas or places, that also have WiFi, or a wired connection you can use.....and you get the same results NO MATTER WHERE YOU TRY. Interet cafe, Starbucks, McDonalds, Public Library, etc etc.
Is that correct?
Maybe try going to the current Update 10.12 (Sierra)
This is a very difficult thing to troubleshoot. I need some background.
Have you always had this MBPro 2013 since it was new?
Or did you just acquire it?
Well, the last resort would be to REinstall OSX.
Yes i know this is not the result you wanted.......but it does solve many issues.
I have noticed in my 10+ year career in computer repair, that computers hat sit OFF for long periods of time suffer wierd anomolous issues.
Speculation is that condensation has set in, due to lack of air movement.
Also, computers that sit out of sight, can be prone to unknown damage. maybe a box falls onto it, or its in a box that gets dropped.
If this machine sat for a year or more, without being used, its very possible this could be the case.
Reinstalling OSX, which is a task in and of itself, will allow you to rule out a software issue, and begin to narrow in on a ardware issue.
Have you run any diagnostics on your CPU, or RAM, or MoBo?