I don't believe the Ryzen 7 2700 has integrated graphics, so you'll need to install a discrete graphics card. Sadly most modern cards no longer have VGA support and most don't even have DVI-I support. So if VGA support is a must you might have to opt for an older card or see if you can't find a converter of some kind. A lot of cards though still have a DVI-D connector though so you should be okay there.
Thanks for your comments, James. Yes, the Ryzen 7 2700 "processor" including a graphics card was definitely my bad. I think I may have a handle on what's going on now, but I'll know only after I try installing my new graphics card it this evening. You were absolutely correct about the output ports. I bought a MSI Geoforce GTX 1070, and it has three Display Ports, 1 HDMI port and 1 DL-DVI-D port. So, I bought a DV1 to DVI-I adapter and a DisplayPort to VGA adapter and hope those will do the trick. Fortunately, my computer is much younger than my monitors, and it seems to have all of the PCI Express slots and supplementary power connectors that the newer graphics cards mandate. Well, at least I hope.
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You should be fine, the new motherboard and power supply have all the necessary cables and ports to fit a GTX 1070.
Just be sure to get a decent branded 550Watt power supply.
Also remember that the GTX1070 have only one of it's output convertible to VGA signal with an adapter.
Not sure that all the displays outputs support the VGA signal, hence you should look for the adapter that is suited for the port.
If i remember well, the only port that could output VGA is the HDMI, so you would need a HDMI to VGA adapter to use you VGA monitor!
The DP to VGA would be an active adapter, these are not as cheap as a simple HDMI to VGA adapte.