It depends on why and what---why there is damage there and what the damage is. Maybe $300-$500 plus the cost the new window if there's no significant hidden issues encountered and it's a fairly straightforward install.

Basement windows are mandated by code as a means of emergency escape. You would not be allowed to close it in.

How many are you mandated to have? These windows are not large enough for egress, and we would not be eliminating all of them.

The usual code requirement for an "emergency escape and rescue opening" (code required "egress" is by corridors and stairs) is relatively new to the IRC and most other codes so if the house was built before that was added to the code in your area, one of these openings is probably not required (check the code). But if that is the case, you cannot remove an existing previously required emergency escape window from a basement bedroom or remove any bulkhead door.

A new emergency escape window/door would be required if you added a bedroom to the basement under a code that required it. Also, if there are existing bedroom spaces in the basement you cannot reduce the window openings below the code requirement for the natural (or mechanical) ventilation for the code in effect when it was built.

But the code shouldn't matter. A basement bedroom should have adequate natural or mechanical ventilation and a way to get out in case fire and/or smoke blocks the egress path through the house. The code just sets a reasonable standard for doing that but you might want to make the space even safer and more comfortable.

Removing basement wondows depends on how they are installed.

If they are metal windows set directly into mortar joints the ony way to get them out is often to saw the bottom, pry it up, finish the cut through the now exposed fin, then pry the bottom up on each side, then the sides pry onward, and the top down (cut if you cannot just bend it down enough to free).

Wood windows on bucks are much easier.
Cut the nails from the window in to the bucks with a sawzall nail cutting blade and pull the window out.

The bucks can usually be pried out one by one, often sides first, then top and bottom.

Good info, thanks!

I remember watching my carpenter try to figure out how to get a metal basement window out of the brick and block wall it was in.

He was so used to cutting a few nails and pulling a window out, and his lack of knowledge about how windows used to be installed in masonry openings left him scratching his head.

He was stunned and how easily it finally came out when he was shown how.