Yes you are right, it is the "M Pro" version
I downloaded your links and installed the audio driver. The beep continued. I then installed the chipset and checked that the AC97 audio was disabled in the Bios - beep still continued. I havent installed the video graphics card yet.
The model is MT-M 6220-24G, so the drivers should be the right ones. I went to the Accessories - Volume and it still said there is no mixer components installed (same with audio recorder).
I then went to "Sounds and audio" and re-activated several windows sounds, so that the speaker-symbol now reappears - still no improvement.
Also the Hardware-assistant only found me an unknown component which I think I had before. I tried to re-install a driver for it but windows couldnt allocate anything. The is no information whatsoever on it accept in the details it mentions ACPI\ASF0001\2&DABA3FF&0 - but this might not even have anything to do with the audio. So I deactivated the device.
I googled that and I came up with this link
http://www.experts-exchange.com/Software/System_Utilities/Drivers/Q_22616462.html"IBM Alert Standard Format".
Alert !? Hmmm... sounds like it could do with the beeping noise.... I'll install the drivers under
http://www-1.ibm.com/support/docview.wss?uid=psg1MIGR-43364 and let you know if this works.