Unsurprisingly, we can't read that - any chance of a translation?
Please open up the file setup.log in the Rome /logs/ directory with Notepad, and search for "checksum" - paste that line only in here please.
We should try a reinstall but the process is different - did you buy this game from Steam, or elsewhere?
If Steam: uninstall the game, manually delete all Rome-related files and directories from where Steam placed them, then re-install.
If non-Steam: Uninstall the game, and then manually delete the game directory - this is important. Reinstall Rome:Gold - choose a new directory like c:\games\rome instead of the suggested path. Download the 2.32c patch, and run it to install it; make 100% sure you point it to that same new directory above so that for instance the new rome.exe overwites the old one, the new romegame.exe overwrites the old one, and so on. Once done right-click on the game's desktop icon and set it to run as administrator, and to disable desktop composition.