Please follow these steps to get magento customer login working.

1. make sure

<input name="form_key" type="hidden"
 value="<?php echo Mage::getSingleton('core/session')->getFormKey() ?>" />

is there in /app/design/frontend/default/your-theme/template/persistent/customer/form/login.phtml

2. Go to admin
system > configuration

a. select store
b. click on web
c. click on Session Cookie Management
d. provide cookie path “/tmp”
e. provide cookie domain “your domain name” example “”
f. save config

now refresh your login page on frontend and try login.