I DESPERATELY need iTunes help! Transferring purchases?

Okay, so I read on the iTunes site that if you want to transfer music on your iPod/iPhone to a new computer, one of the ways is to just plug your device into the new computer and click on "Transfer Purchases." As long as they are songs you purchased on iTunes, it'll put it on the new computer. If its music from CD's, then it will erase that.

Right now, I just have iTunes purchases on my iPhone, so I shouldn't have a problem.
BUT, when I go to my "Purchased" playlist on my iPhone, it only had about half of the songs on my iPhone, but EVERYTHING was purchased from iTunes.

What I'm wondering is, will the new Mac computer recognize that everything is from iTunes and transfer it, even if it isn't in that playlist?

I'm really, really hoping so, and I tried to call Apple customer service, and to talk to an actual person, I have to pay because my insurance doesn't cover it anymore. Which is ridiculous.

So anyone who knows, Please Help ME!
Will All my purchases just transfer!

You'll transfer the songs from iPhone to new computer without erase anything on iPhone if you use leawo iTransfer to do it, and you'll no necessary to pay for the songs with this way.

When it comes to how to transfer video or songs from ipod to computer, we have to use a third program called ipod to computer tranfer tool to help us. For mac user, here i just would like to share you a tool called Amacsoft ipod to mac transfer, which is really an all-in-one tool for iPad users. This iPad Transfer Mac can help you backup the audio, video and image files on iPad to Mac. With this useful tool, you can also batch export your iPad Music, Movies, TV Shows, Podcast, Audiobooks, Books, Ringtones, Playlists, Voice Memos, Photos, etc. To Mac for backup.

Related guide:
http://www.slideshare.net/linsu39/how-to-transfer-photos-from-ipod-to-mac-13514905

I've noticed iTunes does not necessarily continue to offer the same music so it is possible that the music that didn't transfer is because it's no longer available via iTunes and hence download.
I'd suggest picking 4-5 songs that did NOT transfer and search for them in the iTunes store. If they are available, contact customer service as I've read that others have had the same issue.

However if they are not available anymore thru iTunes and all your music is not on a computer in your possession (if so you can use migration assistant) than a reliable third party app may be the only avenue of transferring your music.

It's a bummer to invest $$, and than not get all of the music, because iTunes no longer offers the music. And in my personal opinion, it is misleading of Apple to say the consumer can transfer all the music without mentioning the caveat of the music still and actually being available through iTunes.