Normally, your Adagio Consultant would help install Adagio on a new computer to help avoid things like this.
Did you re-install Payables on the new computer or just copy files over from the old computer? What happens when you choose "Maintain Specifications" from the Adagio Payables menu? Do you get an error message of any description? If the Designer opens, but then you cannot open any specification, then that's a different problem.
The specifications are stored with your Adagio Payables data. If Adagio Payables is running there normally would be any further need for adjustment.
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Andrew Bates