Government is generally immune to negligence law suits. Specially when the issue in question pertains to "discretionary powers" of government.
Otherwise also, for negligence suits (even againt private persons) you need to show personal injury or property damages. Pure economic loss (lost job...) etc. are not enough.
Since the law does not explicitly state that INS will have to process an application in certain time frame, the only other avenue left is "writ of mandamus". In "writ of mandamus", you basically ask a judge to order a public agency or governmental body to perform an act required by law when it has neglected or refused to do so.
Now, INS neither refused to perform nor neglecting (???).
If they have not acted on your petition for years while they keep processing the petitions received by them much later, I think you have a case.