Try cleaning the connections of the SIM slot with a folded piece of paper dipped in etanol or put a couple layers of sticky tape on the back of the SIM to see if slightly more pressure on the contacts will help. You may need to replace the SIM slot assembly
The SIM slot assembly is available - [http://www.amazon.co.uk/Samsung-Galaxy-GT-i9300-Memory-Replacement/dp/B009X6994U/ref=pd_vtp_ce_1|HERE] is one example and there are listings on eBay also.
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[http://www.youtube.com/watch?v=m_oL1cy0g-Q|THIS VIDEO] may also assist you
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[http://www.ifixit.com/Guide/Samsung+Galaxy+S+III+Disassembly+%26+Assembly/9413/1|THIS VIDEO] may also assist you
Try cleaning the connections of the SIM slot with a folded piece of paper dipped in etanol or put a couple layers of sticky tape on the back of the SIM to see if slightly more pressure on the contacts will help. You may need to replace the SIM slot assembly
The SIM slot assembly is available - [http://www.amazon.co.uk/Samsung-Galaxy-GT-i9300-Memory-Replacement/dp/B009X6994U/ref=pd_vtp_ce_1|HERE] is one example and there are listings on eBay also.
[http://www.youtube.com/watch?v=m_oL1cy0g-Q|THIS VIDEO] may also assist you