The power button problem sounds like a hardware fault with the power button and/or the ribbon it's connected to, and from a quick google it seems that power button issues are somewhat common with this model. Is it possible that any water/liquid penetrated the external case (the symptoms you report could happen if any of the switch contacts are randomly shorting this could happen, and water ingress could be one possible cause). There are some "self repair" videos on youtube (just search for "desire z self repair"), but they are not particularly easy..
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e.g. http://www.youtube.com/watch?v=6UtNU8n0MKI
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Not sure what you meant by 'I can only hear caller through the loudspeaker' - that doesn't sound like a headphone problem at all (if headphone was plugged in, you would NOT hear the caller through the loudspeaker).
The power button problem sounds like a hardware fault with the power button and/or the ribbon it's connected to, and from a quick google it seems that power button issues are somewhat common with this model. Is it possible that any water/liquid penetrated the external case (the symptoms you report could happen if any of the switch contacts are randomly shorting this could happen, and water ingress could be one possible cause). There are some "self repair" videos on youtube (just search for "desire z self repair"), but they are not particularly easy..
Not sure what you meant by 'I can only hear caller through the loudspeaker' - that doesn't sound like a headphone problem at all (if headphone was plugged in, you would NOT hear the caller through the loudspeaker).