I know it's a pain but try reading this I know it's not the only place I've seen this issue, but it's the best example I can find. I'm positive I've seen this over at the TT forums.
Are you running Reaper as Administrator? Window7/Vista sometimes has drag and drop issues due to this. Right click on the reaper .exe (by default it is in C:\Program Files\REAPER) and click 'Run as administrator'.