Mac Mini 2011 shows a folder with question mark

Question

Good morning,
I reinstalled last night lion newly via recovery mode (internet) and somehow the internt connection was lost at night. So I tried it again and the installation of lion stucks after all was finally downloaded and the mac mini has booted up again. I see only the text "installing" and a progressbar below, nothing else.
When I try to start the mac mini normally I see only a folder with a question mark.
So, what to do?!
Greetings and thanks for the help!

Answer 1

Reinstalling Lion Without the Installer
Boot to the Recovery HD: Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alterhatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the main menu. Repair the Hard Drive and Permissions as follows.
When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list.  In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive.  If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the main menu.
Reinstall Lion: Select Reinstall Lion and click on the Continue button.
Note: You can also re-download the Lion installer by opening the App Store application. Hold down the OPTION key and click on the Purchases icon in the toolbar. You should now see an active Install button to the right of your Lion purchase entry. There are situations in which this will not work. For example, if you are already booted into the Lion you originally purchased with your Apple ID or if an instance of the Lion installer is located anywhere on your computer.