Yea, I would start by cleaning the MAF. You should probably use 84LX89GT's method rather than my "use a rag gently" method

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That sucks you have replaced so many parts. It may seem like a pain, but it is always better to figure out what the problem is first. You probably have replaced several things that didn't really need to be replaced.
For future reference, you can buy a scanner to pull codes yourself at any auto parts store for around 20 bucks. Guys on this board can help tell you what each code means when once you get them.
Anyway, try cleaning up the MAF and checking its voltage.
Also, since you said the car ran just a
little better when you disconnected the MAF, be careful not to jump to any conclusions. Do you think that if the MAF was left off longer that the car may have died anyways?