Meanwhile, I found out Vista is the last officially supported OS for this computer. As I also have a Vista license I installed it and it's running fine.
I think I'll try Windows 7 again soon. I think it would now work.

I adjusted BIOS settings and I reattached the SATA cable. It seems it did the trick.

Thank you all for your help!

gregrocker said:
I'd wipe the HD with Diskpart Clean Command which solves about half of these failures by cleaning the boot sector of conflicting code.

You can move the data off to external using the installer with Copy & Paste - in Windows Recovery Console.

If this fails predefine an Active partition for install using Step 2.2 in SSD - HDD Optimize for Windows Reinstallation, then from installer's Command line run Disk Check

If that fails test your HD using maker's HD Diagnostic extended CD scan. If none then use Partition Wizard CD Partition surface test which can also Quick wipe the HD and create a Primary NTFS install partition to Modify>Set to Active. Run Partition Wizard Check File System before trying install.

If those all fail then enter Device Manager to disable any devices in error (!) to complete install then update them from desktop using Windows Updates. Device Manager - Access During Windows 7 Installation
Automatically deliver drivers via Windows Update (Step 3)
Thanks for these steps! As I'll try installing Windows 7 again, I'll try these. :)