Contracts are really just instruments to use if and when you go to court because its negotiation and salesmanship that keep customer's happy and enforcing contract terms is what lawyers get rich on.
It sounds like the client has changed your (verbal) contract with them without advising you.
I think the decision is your's alone to make and will depend on your relationship with the client and how much you are prepared to loose. If its 4 months and still no payment - I tend to feel its a lost cause because even the worst companies pay within 120 days or become a member of a collections team. The other consideration is your reputation: when companies learn they can exploit you, they will continue to do it.
If after trying to collect you determine its a relationship you are prepared to loose, I would invoice for a pro-rata period of time used now, and if they won't pay, put them in collections. While collections rarely get's results, they will have a mark on their credit and that can hurt them.
Again - that's the hard line - and your last choice. I would start by phoning today and asking for payment politely and see where that goes, follow up immediately with a past due notice, and hammer away for 2 weeks with a phone call every day if they don't pay after that specified period of time. If you can, show up at their office. Be persistent - but don't threaten action unless you are 100% committed to following through.
Yes, its aggressive, but squeaky wheel gets the grease - just sitting quiet and waiting is what they are counting on.