How can I raise the floor of a sunken room level with the surrounding floors?
Without pictures, if there's floor joists/subfloor under the carpet/hardwood/vinyl, etc., it sounds like it would be as simple as just "framing it in". In other words, you'd just add some 2x4s on 16" centers (with top and bottom plates - kind of like a 2x4 wall that is just placed horizontally) that would raise it to the level you want. Note that 2x4s are only 3 1/2" wide, so you'd need to add 2x4s then some 1/2" plywood on top of that as a new subfloor. Then you could finish that with a floor covering like vinyl, carpet, hardwood etc. You'd need to make sure the new "floor" of 2x4s/plywood (or even 1/2" osb) matched the level of the floor you're trying to match. You'd need to make sure you secured the 2x4 addition with toenailing or buy some angle iron to nail into the side of the 2x4s, and then to the floor. But this is all based on if the floor that's there is made of wood. It would be best if you could verify the location of any joists below the current floor because it's best if you nail the new 2x4s to something solid.

If it's a concrete slab, you could do something similar but would need to use treated material so it doesn't rot, and secure it with concrete anchors.