This is by far the wisest route on the issue. I would just add that you "could" notify your legal department of it and leave it to them to handle. It is their responsbility to deal with legal issues of all kinds. For your part you just need to make a reasonable attempt to resolve the situation through your appropriate chain of command. If they arean't interested document your findings and move on.
If you bring this up and the BSA comes callign when managment doesn't act your almost garanteed to experiance some kind of retaliation.
As someone who works with Asset software i garantee the effort of cleaning up your asset's and tracking everything is well worth it. You could always pitch the cost savings of such a system by reducing waste and overpurchasing.
Your ability to get into a good IT career will always depend on your experience and personality. Technology is unique as achievment is based on your passion and willingness to learn. It is possible to find a good job without a degree, but propably not your first job. To begin you should seek an opening position in some form of IT support role like tech support, helpdesk, call center, etc... This will help establish yourself and provide proof of your willingness to do the work.
Don't let people discourage you, a real interviewer knows that in today's world there's more to an employee than a degree or fancy resume. A resume only gets you a conversation, the rest is up to you. If you can prove you have a compatible personality and relevant experience then your on the right track. Anyone who is so close minded that believes a degree is the only way to prove your worth, is probably not the person you want to work for.
Innovators are born, not learned
Term, holidays, term, holidays, till we leave school, and then work, work, work till we die. -- C.S. Lewis