Missing Contacts, Found if Dialed

On my iPhone 4, when I search for some contacts that I had previously stored, or type part of their name, they do not show.

If I dial the complete contact's number and call, it will resolve and show the name, so I know the contact is in there.

I have a few email account, gmail, yahoo and iCloud. I had an Exchange account, then removed it. I added the yahoo last, not sure if either of those did anything.

I tried to troubleshoot. I went to settings, ... Contacts ..., the default account is "from my PC". I changed it to iCloud, the other option, no change.

Why is this happening and can I recover these "missing" contacts?