Great question! Let me first answer by saying NO you should NEVER give up. ANYTHING and I do mean ANYTHING can be figured out with enough energy and time. So let's continue.
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It could be either one. Your phone or your sim card. The best way (in my own opinion) to test a sim card is to call your phones carrier using another phone so they can have you run tests. So if you use Verizon call them up, Straight Talk, Sprint, Etc, call them up. They can actually diagnose a lot better than you or I can. In addition you can make the call toll free and do not need to obtain an additional sim card.
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However they may just tell you it is the sim card because your device isn't registering the sim card. In which case as @avanteguarde stated your next step would be to acquire another sim card that you KNOW works. The issue with this is, its more work than making a phone call.
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First you will need to find a SIM card that works with your phone, and carrier. Then you need to have your carrier activate the new SIM card in order for it to work with data etc. Then after that if it doesn't work, you will either need to reactivate the old SIM (if you borrowed sim card) or think about replacing the phone / part.
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Now if it comes down to the phone needing repair we have three options. Junk the phone, Send the phone in for repair, or do it yourself and un-solder your SIM card reader and solder a good reader in it's place. Be warned the motherboard my just be faulty in that area, in which case replacing the reader does no good, you will need to replace the motherboard.
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The good news to that is, motherboards are much easier to replace then to start soldering and un-soldering things. There is no official motherboard replacement guide, however there is a tear-down guide that if you watch carefully, could use to identify your SIM Card reader and replace it as well as the motherboard. You can find that [guide|67197|here.]