If you have no access to the other computer because it is dead, then you will not be able to get all of your maps back. You can get some of them back by purchasing support ($4 for 1 month), which will allow you to search ranked beatmaps that you have played on the website. Otherwise, you just got to search through the lists again.
This forum is supposed to be for non-osu! related topics only. This question would be better in the Help forum which is for technical issues and bugs