The search button is the magnifying glass that in the top left next to your account name and picture.
The power button is in the charm bar then setting then power.
I've got the same issue, search but no power button.
If you look on Microsoft's website about the update it does state that some pc's won't get the power button on the start screen, but being Microsoft's own product you would've guessed that the Surface would.
They stated that devices/tablets less than 8.5" won't get the power button, besides my Surface 2 is 10.6".
Why is this happening to me?
That really does suck ��You do NOT SEE that power button on any TOUCH TABLETS. That is what I'm reading everywhere.
We were told last week at BUILD that the power button will not show up on touch only devices (Surface RT and Surface 2 are considered touch only devices). Now, how does Microsoft define touch only devices is anyone's guess.
Devices that don't come with an attached keyboard.
There was some confusion during the beta about why certain PCs have this button and some do not. But here's the answer: Its appearance is keyed to an internal setting called the Power Platform Role that PC and device makers must set accurately in order to obtain the Windows logo. If this setting is configured as "Slate," the button will not appear, because it would be too easy to tap accidentally and tablet users are comfortable with the edge-based UIs. If it is set to "mobile device," as a laptop or Ultrabook would be, the button will appear.
In other words, it has nothing to do with the availability of features like multi-touch or Connected Standby.