After analyzing the inside I`ve discovered the following parts:

• Motherboard: HP Opal-GL6E (also known as Asus K8AE-LM)
  Format: Mini-ITX
• Powersupply: 108 W
• Memory: maximum 1 GB DDR1

The motherboard format (m-ITX) aswel as the small PSU (108W) reduced the possibility to upgrade to new 3rd and 4rd generation Intel Pentium/Celeron CPUs.
This led to the choice of either an Intel Celeron 847 (NM70, HM70), Intel Atom D2550 (NM10),AMD Fusion E-350 (A50M), Intel Celeron 1007U and Intel Celeron  1037U.

The Celeron 1037U clearly wins in speed and function set compared to the others. This reduced motherboard availability to a couple of brands, of which I chose Gigabyte. This narrowed things down to three motherboards, all starting their names with GA-C1037UN and available within in the same price range (around 75 Euro).
The difference between the GA-C1037UN-EU and the GA-C1037UN  is that the EU has passive cooling and the normal version active cooling. I preferred the cooled equivalent because of the already present huge cooler.
Another benefit of the gigabyte motherboard compared to others is the IDE controller. This saved another 20 Euro on a new SATA CD/DVD drive. A downside is the lack of no USB 3 ports.

The next step is memory. The price difference between 1333 and 1600 MHz is minor. As RAM I choice Corsair and ended up with 4GB DDR3 1600Mhz Memory Module (CMX4GX3M1A1600C9).

After assembly I found  out that the PSU contains a miniature ATX 24 pin  supply and I had to find a mini-ATX to ATX converter cable on eBay.