Windows computers only support Miracast, which has only so-so support by Roku. Also, there is specific PC hardware requirements for Miracast to work. As I recall, it requires specific support in the wireless card, and also the video card. Most people find their computers are lacking one or both.
I've connected computers to TVs often with HDMI, and never had an issue. However, I've never used an HDMI to VGA adapter, so your new set might not like it.
Nvidia Shield, Roku Stick (3600), Ultra (4640), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.