CHICAGO — Crunching the numbers on college costs has been a particularly grim task for parents of incoming freshmen this year.

The weak economy has strained their cash resources and the nationwide mortgage crisis has made many unwilling or unable to tap home equity. On top of that, dozens of lenders have stopped issuing federally guaranteed loans because of the credit market turmoil.

“In terms of parents paying, there’s more stress than I’ve ever seen,” said Valerie Broughton, a Minneapolis-based educational consultant who says many are considering changing to less expensive colleges or universities than planned.

Even with the start of college just weeks away, however, money can still be found for those who don’t have all the financial aid they need. One reason is that schools, too, are under extra pressure and working harder to fill their freshman classes this year as students make late switches because of costs.

That can work to the advantage of those who have been accepted to their school of choice but are struggling to pay for it. Additional financial aid and scholarship money can be dangled at the eleventh hour as earlier enrollment commitments evaporate — a phenomenon known as the “summer melt.”

“The later in the year we get, the more valuable each student becomes and the harder they are to replace,” said Lynn Nichelson, director of financial aid at Illinois Wesleyan University in Bloomington, Ill. “The quality student is in demand all over the place.”

For starters, experts recommend contacting a college’s financial aid office before ruling a school out because of money. Sometimes the aid outlook can improve from what was offered, perhaps because of a change in the family’s situation such as divorce or a loss of a job.

It worked for Debbie Bloss, who checked back with her son’s second-choice school, Drury University in Springfield, Mo., so late that fall classes had begun. She had little option; her son had decided after five days at his preferred college that it wasn’t for him, walking away from a nearly full scholarship to enroll at pricier Drury instead.

Drury had given out all its need-based grants for the year and it was too late to search for outside scholarships or grants. But by working with the financial aid office, Bloss and her son were able to obtain a $400 federal Pell Grant, a $1,500 state grant and $500 in academic money, amounts bolstered by $6,625 in federal Stafford loans.

Along with an additional $13,500 in private loans, that was enough to get her son through the first year. The following year he started the process much earlier and secured much more federal, state and Drury grants along with work-study aid, so he reduced his loan amounts considerably.

Bloss, of Blue Springs, Mo., called the financial aid process “very daunting” but “very rewarding in the end.” Her son enters his senior year this fall.

“You really have to do your homework” on grants, loans, scholarships and eligibility, she said. “It’s a lot of work, and it’s painful because there’s a lot of reading, a lot of investigating, a lot of understanding involved. And the key is finding someone in the financial aid office who’s willing to take the time to help you get all you can get.”

Some evidence suggests schools are more willing to help out with aid this year than in the past. Broughton, previously an administrator for several universities, says colleges are dipping into their wait lists more than ever before as a consequence of the trend away from early decision programs, which has resulted in a late scramble for students.

One “must” for those who haven’t already done it is to submit the Free Application for Federal Student Aid form. The FAFSA is required for eligibility for student aid programs such as Stafford and Plus loans and is used by most states and many private colleges to determine financial aid.

Searching for last-minute scholarships and loans at online sites such as FastWeb.com and Finaid.com also can be fruitful. But parents are advised by experts to consider noneducation-based loans only as a last resort because of extra costs and the need to start paying them back immediately.