Hi sosayelbes,
actually you don't want to "convert" but to "record" what your instrument is playing the exact same way as you can hear it on the instrument.
Yes, the midi can be played and converted on the pc,
but your pc and
neither any professional program have the exact same voices as the psr 3000 so it will re-produce the sounds differently and of course you will have the bad results you have already encounter.
So, actually you want to "record" what you hearing when you push the song(midi) play button ON the psr 3000.
First and cheapest move is to buy the cables that overover suggested.
Once you have the cables you will do a recording on your pc to see the results.
(Do you remember the double tape/cassete players we had? The 3k will be the "play" tape and the pc will do the "record" tape )
If your computer is older than your 3k maybe the results are not to your liking or maybe it is unable to even to perform a recording(which I doubt).
The easiest way to record something on your pc is to use Audacity which is a kind of a simple program.
If you want much "pro" results and much better quality because your computer is too old or for whatever reason, that is when it is better to buy also an audio interface.
In my humble opinion, start by buying just the cables and we can help you with the recording even though we are not seem to be that good in educating people about technical stuff