Goldi >>> My Bad. I didn't realize that was such an old model of keyboard. By all means continue to advise the OP on the subject.
BTW, MIDI is not plug and play. Your MIDI USB adapter should be a class compliant device and should automatically be detected and installed when recognized by windows.
On the other hand, unless you are using some weird Yamaha specific software, the actual MIDI keyboard would and should not be automatically detected by most MIDI software. This information must usually be configured manually for each software (Sequencer, Patch Editor, Patch Librarian, etc.) that you are trying to use with the keyboard.
Also be advised that while the official MIDI standard specifies that MIDI OUT should always be connected to MIDI IN, some of the cheaper USB interfaces actually reverse the connections, just to add to the confusion.
Furthermore, the process can often involve having to adjust settings on the keyboard itself as well as in the MIDI software on the computer.
You said that you managed to get some output with IN-IN OUT-OUT configuration, so that is probably the right configuration for this particular interface.
I'm not familiar with the program "Synethesia." Is it a MIDI sequencer or a MIDI Song Player or something else?
At any rate it has very limited MIDI settings on the keyboard itself, only five functions listed between pages 58 and 62 of the manual.
http://download.yamaha.com/api/asset/file/?language=en&site=my.yamaha.com&asset_id=10816
Of those settings, PC1 and PC2 seem to be stock configurations aimed at working with their own particular software.
My advice to you is to use third party MIDI software and leave the PC Mode setting to OFF. The OFF setting seems to be a proper configuration for working with most third party sequencers and player software.
At any rate, sometimes it simply requires some trial and error to get a particular keyboard configured properly to work with MIDI but you really only have a limited number of permutations to try before you get the sounds out of it that you want.
More importantly, make sure that your MIDI software is properly configured so that it recognizes your USB MIDI interface and then set the keyboard type within the software as GM (general MIDI) or XG (Yamaha Specific) and it should be able to work fine at that point.
You might also want to do some googling on how to use MIDI software and check out some instructional videos on Youtube if you still have no idea what exactly you are doing.