Tripoth,
The easiest thing to do is to just copy the station flags from a working phone to the non-working phone.
If you don't want to do that you can go to System > Phone Related Information > Flags
Make sure you have the extensions in the following folders
Expanded CO Call Information On Displays
Outside Party Call Information has Priority
There are a couple of others flags that deal with Caller-ID depending on your version, but these two are the ones that control whether or not you see Caller-ID from a CO Trunk.
Thanks,
TE