Should I change the sentence,"Friends come to me........... " to something like..... "Co-workers come to me with questions pertaining to work."
In short...no.
I agree with Dweezel in that cover letter should be succinct and concise. If that sentence doesn't work for you, then remove it and expand elsewhere.
I think a good sentence to expand on is the bettering yourself one.
So you went back to school, presumably to enhance your computer skills, from what I can tell. That's great. As a reader, that means that you are willing to continually learn new skills, and have the discipline to return to class to do so.
Also your previous work experience...what have you taken from that? (Notice I didn't say "What did you learn?")
What did you take from previous jobs in product distribution? Meticulousness? Saavy for product cycles and purchasing decisions?
What did your lab monitor job show you? Responsibility and assisting others with their needs (taking ownership for your actions and selflessness?)
End your letter with a specific request. Not "I certainly look towards exploring this further". That's too vague.
How about "I would be most delighted (pick whatever suits your personality) to discuss my experiences and qualifications further, either on the telephone (not phone...that's slang) or in person at your convenience. Thank you for your attention and consideration."
The checkbook balancing thing doesn't do it for me. If it's not directly related to the position you're applying for, don't put it in. Keep to the point.
Hope this helps. Good on you for asking for help. It's not an easy thing to do when it comes to this sort of thing.
Kerry
P.S. Let us know how it goes, OK?