I assume you mean WiFi -- though with "wife", it's quite funny indeed!
BBM is a proprietary BB-level service, requiring you to be subscribed to an adequate data plan from your service provider, regardless of the channel you use for it (WiFi versus carrier data network). If, as you say, your data plan is finished, then you no longer have a data plan, and your BB-proprietary services (including BBM) have been shut down. To re-enable, you must re-enable your data plan.
Occam's Razor nearly always applies when troubleshooting technology issues!
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