Songs don't play on iPhone 4 - iOS5.0.1

Question

Why do my songs play on iTunes on my laptop and do not play on my iPhone 4?  Some don't even show up on my phone! I bought Match hoping to overcome that problem; the albums that do not play are in the cloud (I guess) and are in iTunes Store.  Even the ones on my phone won't play.  When I select them, the WIFI appears to be doing a search, then stops, and nothing happens.

Answer 1

If all of the songs you own are already on your laptop, then when you play one, it is the copy on your laptop that will play.  The only time you would play a song on your laptop directly from the cloud would be if it got to the cloud from another computer you set up on your iTunes Match service.  So getting them to play on your laptop really doesn't have anything to do with why they won't play on your iPhone.
Two things may be happening here.  First, if your first iTunes Match session has not completed, you will likely see song titles on your iPhone, but the actual files have not been uploaded from your computer to the cloud.  Itunes first copies your database (which includes song titles) then it determines which songs are matches to ones for sale in the iTunes store and links the song titles you see to those songs.  Then it uploads the rest.  Often times until every song that needs to be uploaded for an album has made it to the cloud, none of the uploaded songs for that album will be available for you to play.
Second, you may want to check the settings for your music app.  There is one toggle that will let you see only the songs that are on your device.  If that is the way it is set, you won't see what is in the cloud unless it is also already downloaded to your iPhone.
You said you guess the songs are in the cloud, but you are not sure.  When iTunes Match is on, you can go into your view options and check the box for "icloud status."  If you sort the new column you will get, you can see what has been matched, what has uploaded, what has been identified as "purchased" (from the iTunes store, and most importantly for you, what songs are "waiting."  Waiting means iTunes Match has not processed them.  Most of the time "waiting" means "waiting to upload." but it can also mean you have one or more corrupted tracks that will keep Match from processing the rest.
I should also mention that you may see songs listed as "ineligible."  Some time ineligible tracks are low-bitrate songs, so low Apple won't allow them in.  You can get around that by highlighting them, going to the Advanced menu and selecting "make AAC version"  Whne you run iTunes Match again, they should either match or upload. 
The other major category of ineligible music is DRM-protected tracks.  Now if your computer is authorized to play them, they should process fine, but if authorization has been turned off, or if they came from a different computer, Apple won't allow them in until you get the computer authorized to play them.  There is a lot of information here on how to authorize your computer, if it comes to that.
Hope that helps you