Have you installed any plug-ins for Photoshop Elements. Generally, when there is a report that a DLL file is missing at launch, it is because Photoshop Elements is loading its plug-ins and that the plug-in is missing this file. Uninstall and reinstall of Photoshop Elements will not remove your plug-ins, they will be waiting for you when you reinstall.
Additionally, you may need to recreate the preferences for the program as well. This can be done by holding down he Ctrl+Alt+Shift keys when you are launching. You must click the keys immediately upon choosing to launch the Editor. You will be prompted with whether you want to delete the settings file, choose Yes.