If my name is on the deed of one house (the deed only, not the current mortgage on the house), can I use the house as collateral to obtain another loan for another house?
When the new mortgage company goes through the approval process they will find that a mortgage is still assigned to the first house. They will be even more confused that your name isn't associated with the mortgage, though they will find your name on the deed.
Without an easy way to foreclose on half a house if you can't make the payments on the new loan, they will not be willing to accept the first house as collateral for the new loan.
The first lender is probably expecting on taking the first house if the that loan goes bad. Each lender would be upset to find that the collateral was lost because of a loan they were not a party to.
Even if you somehow get this by the new lender, if anything goes wrong you will find your self in a sea of lawyers and lawsuits.