What recourse does a former employee have to rectify the failure of a former employer to offer a 401k to the former employee despite availability to all other employees. Should the former employee pursue a claim through the DOL or IRS?

Q: Was the former employee a member of the eligible class of personswho could participate? If the employee was not a member of the eligible group there is no basis for a claim.

Yes, the former employee was a member of the eligible class.

All claims for benefits have to be pursued first through the plan's claims procedures. The DOL might get interested in the claim, but I doubt that it would take the lead if the claimant had not at least started on the right track. Probably the DOL would sit back and see how the claim was handled. The IRS does not care about claims of individuals. The IRS might get interested for purposes of plan qualification (not very likely given that the IRS has been stripped of enforcement budget), but that will not do the individual any good except as a threat to report to the IRS if the plan does not do the right thing. The individual cannot get into court without having gone through the claims procedure of the plan.