The key is in the fact that you said it "worked on other systems with mIRC", and I assume you mean the same version of mIRC, 6.31, and I assume you tested the same file... if so, this proves that the operating system is indeed the factor in the equation as Khaled said.
XP and up should be able to play mp3 files natively without manually installing any codecs at all. That is definitely the case for Vista. These codecs probably come with windows media player for 98. You should not have to download and install anything if you are on XP or above.
You also said it works after renaming .mp3 to .wma.. Sounds to me like it's not an mp3 file to begin with. You can't just rename a .wma to .mp3 (or vice versa) and expect the mp3 to become a wma file-- they have different headers, different contents, etc... obviously trying to /splay a .mp3 file [as an mp3] that *isn't* an mp3 will result in an error. This is not surprising, and definitely not a bug. It in fact should be a clear sign that you are doing something wrong-- not mIRC. mIRC (Windows) probably selects the codec to use based on the file extension; you must make sure the file has the right extension. This is reasonable behaviour, and there is no reason to change that.