Accounting-related positions are GREAT for people in your boyfriend's shoes. Accounting work must be done independently, as you need to access your own brain since that's where the work is performed. So, you often just stay in your own cubicle to complete your tasks (and can even put on your headphones and listen to music while doing it, since -- again -- you have to tune out the world around you in order to accurately do your work.)
If he doesn't have experience in anything accounting-related, it's not necessarily a problem: Amazon sells very inexpensive CD-ROM tutorials for various accounting software -- so all you'd have to do is Google what may be the most popular accounting software used by businesses currently (QuickBooks, for example), and he can learn it at his own pace. If he can master it, he can come in for interviews feeling very knowledgeable and confident -- and even if it opens doors for something entry-level, he can then grow with a company to more and more advanced tasks.
It's okay to be introverted (and who knows? -- maybe that's all this really is at the end of the day). I would suggest he take the Myers-Briggs Type Indicator assessment, which I'm pretty sure can be taken online for free. Once he learns his "type", he'll realize that he's not alone -- and knowing this can really help mentally/emotionally.
Lastly, I can't emphasize enough the importance of cultivating a faith in God as he moves forward on his journey. Many of us are faced with challenges requiring intervention seemingly beyond what we -- or the humans around us -- can provide; fortunately it's always available.
I wish your boyfriend luck, and hope this has been helpful (in full or even in part). If, by chance, he applies any of the above and good things happen for him as a result, please PM me and let me know!