Really? You don't think they are capable of learning the assumptions? This seems kind of sad to me. I feel like with the amount of data being generated now, everyone could use some basic data analysis skills.
I would show them that with a few lines of code they can read in affy CEL files and get a scatter plot (MA plot) with DE genes highlighted in color and labeled (a demo with about 10 lines of code can do this within 10 seconds). I would show them that they can copy and paste that figure directly from R into a Microsoft Word or PowerPoint document (since most of them use those tools daily), or create a pdf. I would show them that they can turn a table of numbers into a heat map with pretty colors. I would show them that they can easily visualize plate based assays (96 well plates) with color, and that they can easily process data from those assays (i.e. fit 96 growth curves, or enzyme kinetic data). I would probably show them that it’s easy to generate and fit a scatter plot first, then show that it’s easy to fit 96 or 9600 scatter plots. Maybe play with some histograms.
Non-visually I would make the following points: R is a language for asking questions. It is the most efficient way to reduce the time between having questions and answering them. This means you can ask more questions, explore your data more, understand your data more. I would talk to them about reproducible analysis, and show them the beauty of how a few lines of code pasted into a buffer makes for (changeable) recipes and documentable and sharable analysis.
The most effective strategy would be to get to know this group's needs then solve a few of their problems thus demonstrating the utility of R. Some tasks that currently are tedious, perhaps require a lot of clicks with Excel could be streamlined and automated and thus become a gateway to R.
Going out there and demonstrating a few neat techniques might work too - the danger there is that after the presentation, once the initial buzz fades everyone will just go back to their familiar approaches since they don't have time to investigate more.