Is there a way to make my apartment complex allow outside cable and internet services?

Talk to the landlord. Why can't you use your phone service to get better internet hookup. Can you set up a dish on your balcony ?

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You are required to go by the terms of the lease, this is often done to control the number and type of wires and boxes that can really look badly

So talking to the owners or managers is all you can do.

You can get better internet service through your phone provider. That's easy to do.

As far as cable is concerned, you may not have any other cable provider in your area anyway other than the one the building subscribes to.

Most buildings will not allow unsightly dishes on balconies due to property damage.