No; you do not pay.
From the Official Rules of Monopoly on the Hasbro web site under heading Mortgages (my emphasis):
No rent can be collected on mortgaged properties or utilities, but rent can be collected on unmortgaged properties in the same group.
To me this is unequivocal - no payment, whether or not denoted as rent, is ever collected on a property that is face down due to being mortgaged. Not carefully the wording "in the same group", and that it does not say "in the same colour group"; thus clearly indicating an applicability to railroads as well as coloured properties.
While an omission from the rules may, depending on circumstance, be regarded as an oversight, I can think of no reason why an explicit inclusion in the rules should not always be taken at face value. Clearly there is an omission about whether or not rent includes payment for landing on a Utility. However the explicit exclusion of payment for landing on a mortgaged utility is clearly an intentional inclusion - so payment is not due under this circumstance.
As the rules never make any distinction on how one lands on a square, to suppose that there is intended to be one for advancing to a Utility in consequence to drawing a Chance or Community Chest card is completely unreasonable.