I would recommend ownCloud. It meets all your requirements including having an HTTP Web Portal, uploading files, downloading file(s), compatible with Windows 10 (written in PHP), and being open source. It also allows an extension where it can play music within the browser and has client software that allows you to sync your music between the server and your computer.
Note: You must use version 7 of ownCloud as version 8+ is no longer supported in Windows. Version 7 does still meet the requirements of the OP's question.
ownCloud gives you web services under your control. It is a self-hosted open source platform with file sync and sharing at its core and available clients for desktop and mobile. The web frontend has apps for Pictures, Calendar, Contacts, News/RSS, Bookmarks, Notes, Music and much more via an open app platform!
ownCloud Server can be installed on Windows and Linux operating systems, and is available via packages, sources, or a one file php installer.