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The best option is, you can copy the contacts from your LG800G to the SIM card and then put the SIM card on your new phone.
On your LG800G, open Contacts app. Press the Options button and touch Settings. Touch Copy and you will see option to copy the SIM to the SIM card. Once you did that, put the SIM card on your new phone and the phone will recognize the contacts. If not, open Contacts app of new phone. Press Options tap (Settings > Contacts) or touch Import/Export. Then select Import from SIM card.
You can also do the transfer from one phone to anothe phone via bluetooth. Let me know how it goes.
I did answer your question. Didn't you get it ?
Here is it again
Sorry, I didn't get your reply. You probably sent the reply to wrong place. Not sure what happened. My apologies for the inconvenience
It is better to transfer via SIM. You already did the first part right. You can cut the SIM and put it on your new phone. You need to get SIM cutter. It is safe to do that. See here --> http://www.amazon.com/Insten%C2%AE-Nano-Card-Cutter-Silver/dp/B00JD9RCNW/ref=sr_1_6?ie=UTF8&qid=1454620270&sr=8-6&keywords=sim+cutter
You can take it to any mobile store to cut the SIM to smaller form. You can even buy the SIM adapter, so you can make it larger if you want to put it back to old phone. See here --> http://www.amazon.com/iPhone-Nano-SIM-Card-Adapter/dp/B009GB6DBO/ref=sr_1_5?ie=UTF8&qid=1454620358&sr=8-5&keywords=sim+adapter
You don't need a special program to transfer via bluetooth. It will work. But it is better to send it via SIM because all the contacts can be easily imported from SIM card to your new phone without losing anything.
From your description, it seems like the old phone has Normal SIM and the new phone has Micro SIM. So all you need to do is, cut the normal SIM to Micro SIM. You can take it to any local store and they will cut it for you. Then put the SIM to your new phone and open Contacts app. It will recognize the contacts. If not, open Contacts app of new phone. Press Options tap (Settings > Contacts) or touch Import/Export. Then select Import from SIM card.