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It should not be difficult to plug the dock connector into the iPhone 3G. (We have 2 iPhone 3Gs in the house, and >6 different cables used to charge them in different locations.)
FYI, the old-style connector (with the push-release clasp) will work with your iPhone 3G as well. If that one goes in easily, the problem is likely the cable that came with your iPhone. If neither inserts easily, the problem may be with the iPhone itself. In either case, you can visit an Apple Store and let them have a look.
Hope this helps...