The fuel not only allows for the engine to run, but it lubricates the fuel pump, and if you run your engine low on fuel regularly, or you run it out of fuel, you risk damaging the fuel pump. You'll need to check the fuel pressure to verify this is the problem, as there may be something else, but I would check this first.
You'll need a fuel pressure gauge that can connect up to the fuel system on your vehicle. For more info, get a repair manual. You might find a free manual here: http://www.autozone.com or go to http://www.alldatadiy.com/ and get an online repair manual subscription. These should have info on the type of gauge and where to connect it, the fuel pressure specifications and other troubleshooting information.
It is possible that the fuel pump is bad ,but I would go the cheaper route and verify that the fuel filter is not plugged. Being that you ran out of gas the sediment often found at the bottom of fuel tanks can cause plugging of the filter. For Fuel pump operation You Might want to check Fuel pump fuse. Some times You might listen for the fuel pump sound by turning the ignition switch to the "ON" postion.
go to www.carsurvey.org/reviews/honda/accord/r129664/ There's a review on that web site which addresses this issue. It begins "At 125,000 miles"; keep reading this review and you'll find out about your problem.