How to fix QGIS error "Entry Point could not be located"?

That's a classic DLL conflict. To resolve it, search for duplicates of the DLL in Windows system folders and rename them to e.g. QtCore4.dll.bak.

In Portugal, the citizen card which offers an authentication and digital signature service that works via browsers puts older qt dll's in windows\system32. Renaming these stops these services from running...

You can copy QGIS Qtcore4.dll and QtGui4.dll to the folder where qgis.exe is placed. This works without renaming the older dll's. The reason this works is the search order used by windows to find the required dll's for an executable. First in line is the executable folder. After that it searches \windows\system32, and only after that PATH is searched.

The solution, translated below, is given on http://osgeo-org.1560.n6.nabble.com/Entry-Point-Not-Found-td3732316.html

On OSGeo4W installing version:

1. Find path: C:\OSGeo4W\bin
2. Copy all files to location: C:\OSGeo4W\apps\qgis\bin\ 

On Standalone installing version

1. Find path: C:\programs (or program files) \Quantum GIS Wroclaw\bin\
2. Copy all files to:  C:\programs (or program files) \Quantum GIS Wroclaew\apps\qgis\bin\