Cant Get Past Mojang screen

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My processor is : Pentium(r)Dual-Core Cpu E5300 @ 2.60GHz 2.60Ghz

And installed memory(RAM): 4.00GB
 
Since there are many mods it takes a bit of cpu power to keep up. A quad-Core of any type should be good as i by my self use i-5 processor quad-core
 
The errors in your log relate to id problems. Is this a base pack or did you add any mods to it. If did not then I would try a force update of the pack.