I finally solved the problem!
In the XP regional settings there is a setup option for non-unicode programs. Even if I formerly set up everything for hungarian including this option, in some mysterious reason it didn't install the proper codepage.
Being totally hopeless, as a final try, I resetted the codepage to some totally different language, applied the settings, and restarted the OS. Opened the regional settings again, set back to hungarian, and what a suprise!, the OS asked for the setup CD, installed the needed files for the codepage. I restarted the OS again and it finally works!
So if anyone meet this problem, first check the regional settings/advanced options/language for non unicode programs!
It should match to that language, which language version of Archicad you want to use. In the add-ons (of course in its localized name) folder of AC13 there is an xreadcfg.txt. file. This file is also for setting up codepages. Check if the DEFWINTOMACCONVTABLE variable is set for the correct codepage.
Happy new year!
Ps.: I still can't understand why the AC10, AC11, AC12 and this add-ons had no problem with this codepage thing...