Method 1:
You can export your data from “Tools > Export” and for ensure export from database and rename old blog folder, then install WordPress in root & active WordPress Network. set url structure for new blog to sub-folder. now create new blog with “blog” name, login to blog & import old blog data.
Your old post in blog and new post in main WordPress. copy old upload folder to new blog upload folder. this method is slightly involved but site run with one WordPress installation.
Method 2:
Move old blog to root (for this method first set blog and WordPress address to new address in settings > general) and create new post type with “blog” name or slug, now install Post Type Switcher plugin and switch old post to new post type. set post type permalink structure to old structure.
Method 3:
simple method you can install new WordPress in root and linked to old page for /contact, /about , etc.