Phone is asking me to plug into iTunes when I power up

Here is the problem....I unfortunately did not back up all my contacts and they are not saved on my sim card. When i was using my phone it turned off on me and I tried to power back on and instead of the phone turning back on like usual it put a symbol on the screen showing me I needed to plug my phone into iTunes so I did and it told that it had to do a restore and it will erase all my data, but before I went ahead with it I some how got it to turn on and work for a while but stupid me didn't back up my info. Now after using for about 4 hours it happened again so at this point I can not get it to work I have to do a restore. So I go ahead with it and it gets to the point where it says waiting for Iphone and never does anything else after that I left it on for 10 hours to see if it worked and did anything, NOTHING I can not figure out what to do? So at this point its trying to do something but then gets to the point where it needs the Iphone to talk back to the computer and never does anything......has anyone else had this problem and what do I do? I haven't had a phone for 3 days now HELPPP PLEASEEEEE