How serious are these symptoms?

I have an eight year old beagle. A few months ago he lost his ability to make his loud, distinctive beagle bark.  Sometimes it seems that it has gotten a little better.  But, recently he has been breathing heavily and even snoring.  I noticed that his stomach felt tight and that he had a lump on the side of his stomach.

[Aleda M Cheng, D.V.M., C.V.A]

You will really need to take your dog to the vet for this.  Any mechanical problem to the throat, such as epiglottal laxity and other tissues, tracheal problems, swelling of the lymph nodes in the neck, some neurological disorders, cushing's syndrome,  and many others diseases may cause barking and vocal cords diseases and the symptoms that you describe..