Actually, Therx, BASIC compilers do exist, and it should be possible to implement a BASIC-like language that is suitable for system programming (the primary requisites being those mentioned by Solar earlier).
The real problem is that there is no real standard BASIC (an ANSI standard does exist, but it is universally ignored). For all intents and purposes, each compiler or interpreter has it's own dialect, some so different from each other as to effectively be diferent languages. Furthermore, few if any of the existing BASIC-like languages are designed for systems programming; most are OS specific and require heavy runtime support. Finally, almost any commercial dialect of BASIC (e.g., VB, Powerbuilder) is going to be proprietary, and trying to duplicate it is likely result in legal hassles.
The practical upshot of this is that you'll most likely need to design and implement your own dialect, and because of the requirements of systems programming, you'd be better off simply designing a whole new language from scratch. You may want to check the
Free Compiler and Interpreter List, and scan through
SourceForge and
Savannah for BASIC related projects, but frankly, your probably looking at a major project just to get the language working.
BTW, what dialects of BASIC do you know, and what qualities of ithem do you particularly like or dislike? It may be that there are other languages which are not necessarily BASIC dialects, but which are similar enough to what you want in a language to be of use to you. Currently used dialects include QBASIC, True Basic,
KBasic, Visual Basic, and Powerbuilder; older dialects include GW-BASIC, Applesoft BASIC, BBC-Micro Basic, and
COMAL.
Also, what other languages are you familiar with? I generally advise fellow programmers that knowing as many languages as possible is a Good Thing; having a broader perspective and range of techniques helps even if you never use those languages to any great degree. I particularly recommend
Scheme,
Smalltalk,
Python,
APL, and
FORTH, as they are quite different from most of the more common ones and can give some interesting insights (though of these, only FORTH is considered to be for systems programming). It is also a good idea to know at least one Wirth language (e.g., Pascal, Modula-2, Oberon) or one derived form his work (e.g., Ada, Eiffel), but most programmers find them to be too verbose. One older language you might want to look into is
BLISS, which is a systems language that was popular around the time C first came out.