If you are really interested with the second position, then give them a ring and let them know of your position now, let them know that you are really interested in taking up the role with their company etc and see what they say. Most will make the decision if they are really interested in offering you the job!
All the best!
老 A (qq:914387753) - 蜗牛!三分五毛的我现在也TMD 学会了奉承。。。反正道不同,也事不关己。。何必劳气呢?
I think Dracoz provided you a very good option. It is worth to try it out.
If I were you, I would sign the offer first and keep looking for jobs I like. I would not be too picky when i were unemployed and would keep "upgrade" my payment and position after I start working.