Can I win the case if the petitioner has not payed the full court fee?

Non payment of court fee is a valid ground recognised under Order 7 Rule 11 of the Code of Civil Procedure, 1908 for rejection of the plaint. However, this ground has to be raised at the inception i.e. in your case, the Trial Court level.

As you are stating the issue of insufficient court fees was raised by you earlier as well, then we need to know what the judge had held on this ground because as per the law, the Judge is required to give time to the party to file the requisite court fee and in case the party fails to do so, then the judge may reject the plaint. 

This position has now been modified by the Supreme Court. The Supreme Court has recently held that non-payment of court fees cannot be a ground for rejecting the plaint. The Court has to give sufficient time to affix the requisite court fees however, if the party fails to do so then the party shall be required to show cause as to why the requisite court fee could not be deposited within the stipulated time.

Now if the reasons given by the party are valid/justified (example: financial distress), then the Court may grant waiver of court fees and direct the party to the Legal Aid Cell for free legal aid so as to contest its claim on merits.

In our opinion, raising this ground in appeal after the decree has already been passed by lower court shall not help your case much. The maximum the Court might do is ask the party to explain why the requisite court fees had not been deposited and give it time to deposit the deficient court fees.