If I discover someone accessed my computer when they had access to it and learn they installed an application designed to break pass codes, but I am uncertain if the passcode breaker was successful, can this be a cause of action in a civil case, and what one?
Yes there is likely a cause of action that can be stated with respect to this conduct, for instance conversion (civil form of theft), trespass or even a species of fraud. In order, however, to prevail in any cause of action you must be damaged in some way. You must show that the person caused you some harm and that you can recover money damages (or injunctive relief if you need it but since you already discovered the software I am not sure how that applies) to recover in a lawsuit. If you cannot identify any damages you should not file a lawsuit. This makes sense in the real world since lawsuits are not, despite what you might see in the media, money making ventures, they are designed to make you whole as opposed to wealthy.
I agree with respect to the requirement that you must have suffered actual damages. The threshold level of proof is fairly low, however, in that even token ( $1 for example) damages are often sufficient. Usually a party in your circumstances has at least some expenses they incurred such as costs to remove the software, to install new security means, or perhaps you lost a days wages to address the problem. The issue of whether you should bring a lawsuit is one to evaluate on a case by case basis. The cost and hassle may not be worth it if the actual damages are minimal. On the other hand, you may have other non-monetary reasons that are more important than simple money damages. Good luck.