I have the feeling you are confused about how parallel processors work. You state your serial code runs faster on your dual core machine than on another single core CPU. That has nothing to do with the fact that your CPU dual-core, but that it's clock rate is higher (and probably also performs more instructions per clock cycle). A dual-core 2.2 GHz CPU indeed doesn't sound like a state-of-the-art CPU, so you would gain some performance running on a more modern CPU (see http://www.cpubenchmark.net/singleThread.html for a single threaded benchmark). On top of that, if you want to process multiple datasets, a multi-core CPU does indeed give you some benefits. In fact, if you do that a lot you might even opt for a many-core CPU such as the AMD Opteron 6000 series (up to 16 cores), even though their single-threaded performance is lower.
If you have to process a lot of datasets, such an upgrade wont cut it. In this case you can try to get computing time on a computing grid , where you can use hundreds of cores simultaneously. Note that again, you will only benefit from this when processing a lot of different datasets. If on the other hand you have only a few very large datasets, you will see no benefit. In this case you'll have to work on dividing your problem to utilize multiple cores at the same time (parallelization e.g. using MPI.
 From my personal experience, most national computing centres run their grids on Linux/UNIX. Since you mention you have an .exe, you'll have to shop around a bit to find a Windows HPC or you'll have to port your program.