Check the wall mount cradle clip under the handsets to be sure it is down for desk phones. Sometimes people like to set this in the extended position thinking it will keep the handset from falling off, but it often keeps the handset from fully hanging up, causing issues like you describe. This was a frequent problem when we first installed IP phones.
http://www.cisco.com/en/US/products/hw/phones/ps379/products_tech_note09186a00801c0810.shtml
The phones are designed with a reversible clip in the handset cradle area. The clip is used with the tab out when the phone is wall-mounted. Check to see whether the cradle handset clip is in the wall-mounted position (with plastic tab that protrude upward). If the phone is on a desktop, slide the clip upward to remove it, rotate one 180 degrees, and slide back in so that the tab is hidden.
This tab can interfere with the handset as it is replaced on the base (in the cradle), which causes the hookswitch to remain in the up position. When the handset is lifted later in an attempt to initiate a new call or answer one, the hookswitch is not activated. If you answer a call, the phone continues to ring; if you place a call, no dial tone occurs.
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Dave