Hello Masha and welcome to Ubuntu!
You can, in fact, install Ubuntu again and replace the broken version on your computer. If you wish to do so, then proceed to install Ubuntu again, but when you are asked to choose where to install Ubuntu, select Something Else. The next screen may look rather intimidating, but don't worry, I am here to help. At this screen, select the row that lists ext4 under the Type column in the chart, and then click the minus sign near the bottom of the window. After, you will note the words "free space" being in place of ext4. Click this row again and then the plus sign near the bottom of the page. A window will appear and in it you must choose "/" as the "mount point" using the selection box in the window, and ensure that "Beginning of this space" and "Logical" are selected, too, as well as "Ext4 Journaling File System" for the "Use as" box. Click OK and then "Install Now" at the bottom of the previous window.
Now, the installation will proceed as it did when you first installed Ubuntu. Let me know if you require assistance.