The line you mentioned looks like this:
$data['checks'] = Mage_Payment_Model_Method_Abstract::CHECK_USE_CHECKOUT
This means Magento cannot find the constant
CHECK_USE_CHECKOUT in the class
if your code is up to date, the constant should be there.
The constant was introduced in Magento 1.8.
The fact that this does not work for you makes me speculate, that at one point, you had an older version of magento (1.7 or below), you had to do some changes in the
Mage_Payment_Model_Method_Abstract and you (or someone else) copied that class to
Because of this, the class in the
local folder is used and it's not up to date.
I suggest checking the differences between the class in the
local folder and the core one from the version you previously had, copy the class from
local (from the new version) and implement the changes in the new class.
Note: This is what can happen when you copy code to
local code pool and you later upgrade.