Sorry for the delay, I'm an early to work person, so I have to "turn in" early to bed!
The answer to your question is yes. With the Briggs engine ( fuel tank fitted to bottom of carb model) The engine relys on its induction stroke vacumm to pull up the petrol from the tank. This is aided to a degree by a very small gasket in the body of the carb.
As the machine gets a bit older, a couple of things tend to happen, firstly the filters that are on the ends of the tubes in the tank become a little blocked, so the amount of petrol "sucked" is lower, and secondly, the compression in the engine becomes a little less, so there isn't so much "suck" in the first place.
It is possable to increase the compression with new piston rings and whatnot, but I find it's much easier to sort out the problem of the blocked filters by removing the tank and stripping and cleaning it all.
A short term fix is to try starting the engine with the fuel tank never less than 3/4 full.
all the best, let me know how you get on.
As an after thought, you have got a spark, haven't you? if you haven't allready checked, put the throttle lever into the run position, remove spark plug, rest it on the top of the engine, attached to the plug lead, and give the rope a good pull. you should get quite a good visable blue spark, if not, you might need to start delveing into the ignition side of things a bit more....
I thought i had better ask, you never know......I've done it myself, spent AGES fixing one problem, for it to turn out to be another....DOH! :roll: