If you are using the trial version of PSE7, you should upgrade to PSE11. Here is the link to download trial version:
Otherwise if you want to continue using PSE7, please try couple of probable solutions as mentioned below:
1. Close Elements.
2. Launch the Photoshop Elements Welcome Screen and hold down ctrl + alt + shift as you click Editor.
3. Continue to hold the keys until you see a message box asking if you want to delete Photoshop Elements settings file; click Yes. Elements will open with default preferences.
Solution 2: In case any network printer is attached try to launch without network or printer uninstall or make different printer as default.
Solution 3: Try launching with anti-virus off or removing PSE from conflicting list.
On the drive on which you have installed PSE,on my machine it is on C:
Go to C:\Program Files\Adobe\Photoshop Elements 7\Locales\<locale>\Plug-Ins\Import-Exportand you will find twain plug-in. Remove that plug-in from that location and copy it somewhere else.
Now launch PSE and check if it works.