so all three parts finished downloading, and then you ran anesis_full_20121103.exe (Part 1) to install the game?
did you get any errors while you were installing that asked you to skip any files?
if there were no errors while installing, check C:\Games\AnesisRO or something like that, if you weren't already looking there. i just want to make sure files didn't end up in odd places. there should be over 100 files and folders in there, among them anesis.exe and anesispatch.exe (they might just show up as anesis and anesispatch depending on your computer settings).
if there were errors while installing, i hate to say it but the files lost a few bits while they were downloading and so they will not be able to install all the files the game needs to run. i suggest you follow the steps here for a more reliable download:
http://www.anesisro.com/forums/index.php?topic=118782.0