The answer to this question relies on several details:
First, what is the requirement driving the replacement of your existing application? You mentioned security considerations. Depending on the depth of those issues, you could take your original code base and perform a thorough analysis on what you need to change and migrate the code forward. If the issues you are having with the old application are such that a migration isn't feasible, then you'll need to start over with a new code base. It is my experience that when doing this you are better off trying not to "copy" the logic in your first application but to start from the ground up and reuse "components" of your existing application where applicable. This will force you to take a fresh look at the application as a whole and how to design your new requirements in.
Next, do the two applications need to live side-by-side or will the newer "replace" the original? If you are able to get rid of the old application when the new one is developed, you can take this time to re-optimize the information you currently have in the database. When old applications have been significantly modified from their original design, the data stores that it uses are usually changed as well and most often, in a sub-optimal way.
Also, I'd look at reducing external dependencies. You mentioned using PowerBuilder to build your original application. With recent updates to the Visual Basic language and toolset, many new features have been added to the language directly that may negate your need for these tools. Adding extra components will most often make deployment and maintenance more difficult.
Lastly, I'd recommend picking up Visual Basic .NET Code Security Handbook by Eric Lippert of Microsoft. This is a great overview of code level security geared specifically for VB developers.
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