D.,
I had my share of breastfeeding issues with my third child and I've used a manual pump, an electric pump, and finally a rented hospital grade double pump. First of all, let me reassure you, as you have found by feeding your daughter after you've tried to pump without much output, that you do indeed have milk in your breasts. It is a myth that you ever totally empty your breasts.
Secondly, a baby is a much better "pump" than any mechanical device we attach to our breasts. IT does take practice. I would strongly encourage you to contact a lactation specialist. I contacted a specialist who was able to identify that my son had a weak suck which was why I had to resort to pumping.
Now, I want to share with you (and anyone else who may read this and be a first time pumper) my experience. Because my son had a weak suck, my milk supply had decreased and pumping was the only way to increase it. When I first began pumping, I was only able to pump 1/2 - 1 oz of milk in a 24 hour period. I was pumping for 20 minutes around the clock, every 2 hours~per my consultant's recommendation. I pumped for 2 months like that when I discovered that the milk I had been pumping and freezing had soured. Every woman has an enzyme in their breastmilk called Lipase. Some women have too much. If you have too much Lipase in your breastmilk, your breastmilk will "sour" when chilled or frozen. The milk will smell funny...and it will taste like vomit. I'm not kidding. I had contacted my lactation specialist immediately and although she reassured me that my milk was OK to feed to my baby, I couldn't get past how awful it tasted. The longer the milk is frozen, the more prominent the taste is. It was upon making this discovery that caused me to stop pumping altogether. The only way to find out if your milk has too much Lipase is to freeze some, un-thaw it, smell it yourself and do the taste test. If it's fine, then do keeping doing what you are doing. IF it is sour, then you have to flash boil your milk before chilling or freezing it.
Contact Le Leche League in your area and a leader should be able to give you contact info for lactation consultants in your area. A hospital grade pump is by far the best way to go. I found a company out of New Jersey and their web site is: www.ecobabycare.com. I found them by doing a basic search and they rent for $49 a month; they rent hospital grade pumps by Ameda. It was an awesome pump (a real workhorse!) and an excellent company to deal with! Good luck with pumping. IT does take time... and practice more than anything. Some women have a natural "knack" for pumping out large quantities no matter what pump they use. Others need help so please seek the advice of someone who can sit with you and watch your pumping technique.