Yes - Macs can be very picky about correct RAM.
If your new RAM is just the one 4GB stick, it may be a mismatch because of a different manufacturer, so...
Try installing the new RAM stick - and remove the 2GB stick. Use your MBPro for a bit, long enough to find out if that works better with just the one 4GB stick. If it works, you just need to buy a second 4GB stick to max out the RAM on a 2010 MBPro.
Your 2010 MBPro standard drive was a 320 GB hard drive. That's the size that you have now, and I expect that it is the original drive.
Windows drivers? I would probably try booting to your Windows system, then open the Device Manager. Click on the Video or Graphics, then go to properties for the Nvidia driver. Then, I would choose to uninstall/delete that Nvidia driver. Your Windows will reboot. Go back into the Device Manager, choose to view changes to the hardware, and check for entries in Graphics/Video that show an exclamation mark. Use the menu to search for new drivers. That should fix it - or you need to simply reinstall the Boot Camp software, which should also get you going (but a 2010 MBPro may be too old for the boot camp software, I don't know for sure. The normal Windows device manager updates will probably do the trick for you. A restart or two, and Windows might be fine (well, as good as Windows can be
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