Sounds like she's depressed! Been there, done that!
Are there any mom's groups around--through recreation department, library, hospital, parenting center, churches, etc.? Sometimes that can make a world of difference. Also, is she on Mamasource or other online outlets? That can do wonders as well. Would she be interested in joining a book group or something like that to get her outside of herself? Is she open to volunteering her time somewhere (some places welcome moms and their kids so that moms can get out). Check the local newspaper or Chamber of Commerce.
Meanwhile, how does she eat and exercise? Can you suggest going for walks to get those endorphins flowing? You can take the kids in a stroller or backpack so you can go at a good pace.
Do you know of consignment shops in the area to help her save money? We have a good income but I still shop at consignment shops for kids clothes, etc. They grow out of stuff before it wears out usually. Why buy new if you can get perfectly good stuff used? Reduce, reuse, recycle! : )
What did she do prior to her daughter? She may be sorely missing being in the work setting with adult conversation. Is she someone who would be better off working part- or full-time? Not everyone is cut out to be a full-time SAHM. That might relieve their financial stress. And if she works at something that only makes enough to cover her childcare fees, help her discern if that might still be worth it for her sanity. It might just be the trick. (It might not be as well, but it's worth discussing.)
Parenting can be wonderful but it can be incredibly stressful. If her self-esteem is tanking, it sounds like your friendship could help her see possibilities she might not have thought of.
I have been on anti-depressants for years. It runs in the family but being a parent highlighted the need for me to finally go on meds. Prior to that, counseling had always done the trick. I know she says she can't afford the co-pays for counseling, but there might be a non-profit that counsels on a sliding fee scale in your area. Sometimes pastors counsel free of charge as well. The trick is taking the step to explore the possibilities. Sometimes knowing you need help can be paralyzing in itself.
It's important for her to understand that if a person continues to be depressed, one's body chemistry can change. The longer she is depressed, the longer it may take to come out of it. My preference is to go to psychiatrists because they have more specific training with medications for depression, but a good general physician might be able to help as well. It might be worth a try.
Another idea...Ocean State Job Lots was selling full-spectrum lights for pretty cheap. If she's near one of those stores, $25-30 might be well-spent. Those lights can normally range from $75-100 or more. I use mine whenever I'm on the computer, especially in the winter. It actually seems to help!
I know it's hard to see a friend in such turmoil. It's even harder to be in that turmoil. If she can get a handle on her own emotions, her daughter might respond very positively to the "new mom". Kids key off of parents' emotions unwittingly. If she can get help, it might help in all sorts of fronts.
Good luck! You're a great friend to ask these questions!