Danielle, you did the best you could. I was in the same position -- I simply could not produce more than a trickle of milk, despite pumping, herbs, and even a prescription medication that increases milk flow SOME but can't be taken for more than about two weeks at a time. Danielle, for weeks I even taped tiny tubes to my nipples, hung a special bottle full of formula around my neck and attached it to the bottles, so my baby could "breastfeed" even though what she was sucking was formula. But after a certain point I would have been denying my child essential nutrition had I tried to stick to breast milk only. You would have injured your child had you not given him formula, plain and simple.
You made a huge effort. You cannot, cannot, cannot blame yourself. In fact, you can be proud of the effort - you didn't give up because it hurt a little, or because you weren't willing to get lactation advice, or because you were inconvenienced. (And please, don't start to blame yourself for potentially poor nutrition as another poster seemed to indicate!)
It is a big concern to me that you say you feel you are not bonding with your second child as well because you did not breastfeed. Breastfeeding is not some kind of mandatory ingredient for the mother-child bond, wonderful as it is. If you see the lack of breastfeeding as some kind of barrier between you and the baby, you should talk to a counselor about why that is and how you can get past it, for your own sake and his. You use the terms "guilty and depressed" which are red flags - you could have postpartum depression that is manifesting itself as "I feel bad about not breastfeeding" when there are larger depression issues happening and triggers that have nothing to do with breastfeeding itself. Postpartum depression can mean feelings that you and the baby aren't bonded, which is just what you're describing. Please don't try to handle these feelings on your own. Call your doctor tomorrow for a referral for help and see someone this week-- don't put it off.
Finally -- have you talked to your husband about this in exactly the terms you have used here? Let him read your posting and then talk to him and ask him to help you help yourself; he needs to be on board, to support you and to watch the kids while you get help and a break. If you feel you're not bonding with the baby, that affects your husband too, and he needs to understand this is more to you than just a wistful "I miss breastfeeding" emotion. Take care of yourself, don't let anyone make you feel guilty, and get help from someone professional. Mamasource advice is great, but cannot replace a trained listener's help.