The failure to recognize the adapter is usually caused by either a faulty adapter or a bad DC jack.  One or the other would need to be replaced;  figure on $30 for an adapter and $20 for a jack.

The plastic parts of the case are inexpensive -- maybe $50 for both -- but the labor involved to replace them is not insignificant in terms of your time (or worse, paying a shop for a couple of hours of work).

If you have to replace the case parts plus the adapter and jack, you're up to $100 -- and that's without the labor.  It's about twice what the entire system is worth as well;  only you can decided whether the system is worth the cost of repair.  You can likely buy a complete used system several years newer than the one you have for less than it will cost to repair this one -- and since Windows 7 is obsolete, the newer system will run Windows 10, which is in-support and therefore secure for use online.