technically, unless you used a different account for your phone than what you do on your computer (I don't see why you would), your droid contacts are part of your gmail contacts. there may be a way to fix it from your gmail on you computer, I'd guess by adding your droid contacts to another group which Calendar is able to take advantage of. or maybe there's a way to get Calendar to use the droid group.
I say this all as "somehows" since I don't actually use Calendar, but I will try it out and post my findings.
update: OK, from your computer, make sure that you use the "Birthday" entry in your contacts, rather than putting the birthday in the contact's "Notes" field (it seems that's only available from GMail's contact manager). then go to Calendar > Calendar settings > Calendars > Browse interesting calendars > More and subscribe to "Contacts' Birthdays and Events" (and any others you may want). Next, on your phone, goto Calendar > More > Calendars. If you only see your default calendar tap 3 times to get it to re-sync, that should get the subscriptions to pop up. hit OK and give it a minute or three.
you'll now see your contact birthdays on the daily and weekly views, but I can't seem to get it to work on the monthly view.
update2: hrm, it was working for 2 minutes. I'm gonna have to guess there's something wrong with the account sync or (more likely) the Calendar app.
update3: OK, it's definitely the stock calendar app. I've just tried the Touch Calendar beta (very much recommendable, actually), and it shows everything just fine.