Is there a way I can play this game on my computer?
Shining Force 2 is not available commercially for the PC. The original Shining Force has been released for the PC in a Sega games compilation called the "Sega Smash Pack 2".
However, that doesn't mean that you can't play Shining Force 2 on your computer ;) It can be played through the miracle of emulation. I don't have the time to tell you all about emulation, but www.zophar.net would be a good place to look for info. Basically emulators are programs that you run on your computer, and they pretend to be a different system, for example GeneCyst pretends to be a Genesis. Games are "dumped" to ROM files (this is done though a device that connects to a computer) which can be played using the emulator.
So, by using a ROM and emulator, you can play the games on your PC.
Remember that although emulators aren't illegal, ROMs are illegal. They're pirated software and unless you own the real game you really shouldn't download the ROM. Of course, since the systems are very old now and the games no longer available in shops, it probably doesn't really matter anymore (although let's not get into legal/moral arguments here!). If you download the ROMs and are caught by any organisation that works against software piracy, on your head be it. That being said, it's quite unlikely that anyone will know you're using it. The decision, in the end, is yours, and I cannot be held responsible for any actions taken against you (or any loss/damage) as a result of using ROMs or emulators.