new battery, no charge, and it wont sync

i have a similiar problem. I just changed my iphone 4 battery last night. and it would turn off and on by itself , decreasing the battery life and wouldnt charge but i didnt care becuase the battery was 65% charged. but it was working pretty normal for a few hours this morning the battery indicated 28% and it died. like...... the percentage doesnt change. i tried to turn it on after it died but then the battery said 1% and that i needed to sync it to itunes which is pretty impossible because it wont sync. so now i have a new battery, no charge, and it wont sync :/ fml i have no idea what to do