Sounds like you either have a bad filter, installed it incorrectly or your water valve might be gone. I just plugged your model number into the Virtual Repairman at PartSelect.com and got a whole list of common problems for that fridge and the most likely solutions, here is the link to the results - http://www.partselect.com/AdvancedModelSearch.aspx?ModelNum=glhs67eepw0&mfgModelNum=&fkMfgID=4
Hope this is helpful!
Rob, July 2011