Hi! I have more than 20 years of experience in software development (since 1996) and I still remember programming for MS-DOS (6.22 was a good version, by the way). Also I have a diploma in Math, so lottery calculations will not be a problem.
Your basic description is quite good, I think the Initial development will take about one week. The bid can be adjusted when we will have full specifications (if they grow of course, not if they are just clarified). We can discuss it in chat before project starts.
On the programming language: I know most of Basic dialects, including QBasic. Depending on your choice the modernized application can be written in Visual Basic, C# or Delphi (all are OK, and Visual Basic is OK, counting that the sources are in QBasic; but if I would really recommend Delphi to keep balance between language features, ease of GUI development and possible extensions like a network versions; the choice is up to you). Source codes will be of help, of course.
Thank you,
Alex.
P.S. I have UK customers who you can refer to for references--they will confirm quality of the final code and services.