iPhone 4 not charge after screen replacement

After 3 days i found the problem, when i make pressure to the battery connector with my finger it works perfect, sometimes for 5 minutes, then the iphone turn off again and no charge.

What can a i do? cleaning it? if i put something in the phone like a EVA Rubber it seems to work, this can broke the screen or something?

EDIT: now i have a new problem, i found that the screw of the battery connector was no properly placed, now the phone shows that is charging but never starts after hours of charging, i try to restore it (whitout the screw) and when i finish if i dont have the screw in place give me an error (cant complete the restore) and if i have the screw in place it finish the procese and then shows again the charging screen with no solution

i need help im from Argentina and here a new battery cost 200 usd :/

if the problem is the battery where can i buy it with international delivery?

Thanks, Milton

(SORRY FOR THE BAD ENGLISH XD)