Sonic007,
If your computer is like mine, then no you would not have to pick between wifi and using this slot that I speak of. The slot would be under the panel that you take off when you need to add or remove ram. The slot on mine is close to the center of the laptop. Again, on my computer there are two panels that can be taken off. The slot is very close to the second panel that doesn't need to be removed to make changes to the ram. Let me know if you have this free slot, because if you do it will greatly help you out...even if you do end up having to reinstall windows, having a SSD in that slot will make your laptop fly if you move the windows install to the SSD so as to boot from it and not the HDD.
With me moving my install of windows from HDD from factory to the SSD (which you can install with or without the slot I've discussed above), I could actually boot a new install of windows 10 in less than ten seconds. Of course, this was after I setup fast boot and UEFI booting within the bios.
Regardless of whether you have the empty slot that I do or not, you should remove the panels and do a simple compressed air cleaning...for best effect you should go further than that and remove the keyboard and clean under it. Heat caused by poor air flow can cause CPU throttling and hence a slowdown.
I have an idea on how to check to see if it is a hardware vs. software issue. Although, I'm almost certain it is software related. Do you happen to have a USB thumb drive with at least 2 gig of space that you don't care about being formatted? The process I describe will not change any settings on your windows machine, and you'll be able to try linux. This will kill two birds with one stone since you said you'd like to try it. Go to this link and download Ubuntu 16.04.02:
https://www.ubuntu.com/download/desktop
Once downloaded, download and install Rufus USB installer at this link: https://rufus.akeo.ie/ Once you've done so, insert your USB thumb drive, and open RUFUS. Beside the "Create Bootable disk using" ensure that ISO Image is selected, then click the disk beside it. Navigate to the Ubuntu file that you downloaded before rufus and select it. Now, at the bottom hit start and wait until done. Reboot your computer, and press F12 repeatedly until the BOOT menu appears. Select USB from the menu and you will now boot into Ubuntu using your USB stick. Whenever anything comes up, make sure to click "Try Ubuntu without installing".
Congrats, you're now using a linux distribution called Ubuntu. Look around and play for awhile. Specifically, see if it is as slow as windows was. Click on the upside down looking triangle in the top right hand corner of the screen to connect to a wireless network. Then, click on the firefox icon on the left and surf the web, see if you have the same issues with speed. Once you're done looking around and playing with linux (which you said you'd like to try) shutdown the computer and remove the USB and at next boot you will boot back into Windows as normal.
If Ubuntu didn't have the same issues with speed and video then it's certainly a windows problem that should be fixed completely without additional hardware by simply cleaning up windows. If you experience video tearing (try putting a DVD movie into the CD-rom while Ubuntu is loaded from USB), then maybe you're having some issues with the video card or intel integrated graphics which could explain the general slowdown. It could also be the HDD, test this by doing a read/write test and compare to speeds of the HDD on the factory specs. Going further, if you experience slowdown and you haven't determined cause yet, then perhaps the cpu or ram is starting to fail. You can test CPU stability and RAM speed by putting them under stress test programs available online.
Rick