You will not need to buy a new version of Windows 10 provided either of the following are true:
You upgraded from Windows 7, or Windows 8x to Windows 10 before the free upgrade offer expired, or
You purchased Windows 10 pre-installed on your computer, or purchased a DVD and installed it yourself.
If however, you wish to upgrade to a different version of Windows 10, then yes you would need to buy a copy. For example, I have Windows 10 Home edition here, so if I want to use Windows 10 Professional, or Enterprise, I would need to purchase a copy.
So it appears you have 3 issues in your opening post?
A blue screen — are you meaning a BSOD error message? If yes, then what error message?
Microsoft Edge will not open
Windows Update issue that leads you to believe you'd have to buy Windows — In this instance are you referring to trying to download a Windows.iso to install Windows 10 or create a bootable disk from, or are you literally meaning the Windows Update Service, where you normally see updates for Windows Defender, Windows Cumulative updates, and updates for other Microsoft products.
If you can clarify we ought to be able to help you get you computer working again.
It would also help if you could let us know what computer and model you are using, and what version of Windows 10 you currently have installed.
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