"In the Defense Department, what you have now are material weaknesses that are in every single area, in every part of the department, so deep and so wide you do not really have any way of figuring out where money is being spent," says Linda Bilmes, a federal budget expert at Harvard's Kennedy School of Government.

Every year, the Pentagon tries to justify its budget request to Congress by submitting three years of financial data: "actual" performance for the past fiscal year plus projections for the current year and the next. But because of the lack of reliable accounting, these totals are largely fictional. That, in turn, raises major questions about whether the government will be able to meet skyrocketing commitments for future spending on ships, planes, and high-tech ground weapons, especially given the expected growth in spending on Social Security and Medicare, and the impact of tax cuts.

According to David Walker, who recently left his post as head of the Government Accountability Office, the failure of the Pentagon's outdated and incompatible systems to keep tabs on expenditures—even as the wars in Iraq and Afghanistan eat up an ever-bigger chunk of the federal budget—puts several Defense Department agencies high on the G.A.O.'s list of federal programs that are mismanaged and prone to fraud, waste, and abuse.

John Evans, a retired Pentagon official who oversaw more than half of the defense budget, says that all this just encourages the military branches to conceal spending. "If you want to know how much one of the services is paying, you have to ask them," he says. "They say, 'Why do you want to know?'" When Evans did a formal review to see if spending was on track, he says "it was like a C.S.I. crime drama to find out where the services spent money and where they squirreled it away."

To enter the Indianapolis center is to pass through a time warp, to a place where the most critical software programs date from the dawn of the computer age. They run on old-style I.B.M. mainframes and rely on Cobol, the ancient Sumerian of computer languages. "This was a bunch of systems patched together," says Greg Bitz, a former director of the center. "I never went home at night without worrying about one of them crashing." Bitz predicts a crisis as older programmers retire. "Try to find somebody today who knows Cobol," he says.

Hilligoss and other clerks sit in long rows of identical cubicles and enter endless sequences of numbers and letters by hand. The strings signify contract terms, identifying information, due dates, and accounting and appropriations codes. Even if the workers input all the information accurately, they can't prevent mistakes and miscommunications down the line. Indeed, the moment they authorize payment, triggering the transfer of money, any ability to reliably trace it disappears.

Since the scandal in 1985, which revealed that the Navy paid Lockheed $640 each for airplane toilet seats, Congress, military leaders, and regulators have agreed that the Defense Department's internal accounting system is in shambles. What's startling is the scope of the problem and the government's seeming inability to fix it. Over the past two decades, the Pentagon has repeatedly tried to design new computer systems to replace the antiquated ones. Even today, new incompatible financial systems continue to proliferate within the services, contrary to directives from the secretary of Defense's office.

In a September 10, 2001, speech, Secretary of Defense Donald Rumsfeld pressed for a top-to-bottom overhaul of Pentagon financial systems, which he later estimated would save the department as much as $25 billion a year. "It is not, in the end, about business practices, nor is the goal to improve figures on the bottom line. It's really about the security of the United States of America," Rumsfeld said, arguing that waste, mismanagement, and overspending on bureaucracy were taking resources away from weapons and troops.