Well, I don't know about showing a pop up window upon the clicking of a button, but you could definitely use conditional formatting on a control to achieve the same thing.
Make a new node: boolShow, attach conditional formatting to the VendorDropDown that hides when boolShow is false. The Choose button will toggle the boolShow to true. After selection is done, toggle boolShow to False.
To get the value to the textbox you could just bind the VendorDropDown and VendorName to the same node, or you could just a function on VendorName to set the correct value. You might want to make VendorName read-only.
I hope this helps you get started! Note that this was all done without code.
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Matt Faus
InfoPath Dev Texas
Matt Faus / Microsoft InfoPath MVPQdabra® Software / Streamline data gathering to turn process into knowledge