Exhaust blower

Your water heat is at an age that I would recommend replacing the whole unit. That one cannot be too efficient and most likely has sediment built up on the bottom of it pretty bad.

Should unscrew and disconnect easily for replacement.
Call manufacturer
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#blower

http://waterheatertimer.org/Water-heater-manufacturers.html

Gene

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Sounds like you're not getting enough combustion air.
If you have a draft motor or blower make sure it is running.

If the blower will not run, then the unit will not fire up due to a safety hazard. If it is a capacitor start motor, then you may have to replace the capacitor, otherwise you will have to install a new blower motor. Hope this helps

theoretically possible-----a mouse can get in, but most exhaust fan bearings are permanently sealed and are expected to run perfect for their designed life, without any need for lubrication---if a mouse got in, i can only assume that it was chewed up (or it's **** /urine) and was pulled into the motor/bearing shaft and caused some slow in revolutions due to animal parts grinding in the smooth bearings ---it could happen--it depends on how the bearings are sealed around the exhaust motor shaft....orrr, the mouse was killed by the spinning exhaust fan blade, and then "pasted" to the fan blades(ironically called a squirrel cage) and this caused extra weight and an unbalanced exhaust fan which would rapidly cause wear and burnout of bearings due to tremendous speed of exhaust fan---i have seen many a dead rodent inside "squirrel cages" (furnace and water heater exhaust fans and their housings)...in fact i chose to even scrape some of them out for refurbishment!

find out if it does the same noise with the venting disconnected

There really is no way to do this. If you put a cap you will restrict the air flow which will cause you to have problems with the water heater, same thing if you where to put screen on it. You can try enlarging the pipe to a 3 inch and see if that works. But 15 years in the trade nothing has been made to reduce the noise

Water heaters with a blower on top - power vent exhaust - have a switch to tell the "brain" AKA controller, that the blower is working properly and that the exhaust vent is unobstructed. First, make SURE the vent is unobstructed. If it is, carbon monoxide can kill you! Second, is the blower coming up to speed quickly or is it sluggish like the bearings are dry? Third, is the water heater in the laundry room and are the fins of the blower are full of lint? If all is O.K. to this point, then check the vacuum switch. It is in the box near the bottom of the water heater. It is round and has two wires going to the center and tube going to it out on the body. The switch has a diaphragm that works the contacts. Is the vacuum tube in good condition at the fan and at the switch? You can take the switch out, hook an ohm meter and a short piece of tubing to it. **** gently on the tube. Does the switch close every time? If it does the controller may be going bad. The problem, you don't know hard to ****. Put a new switch on it, see if it is fixed. but only after you have checked out the first three above!

It may just need a new pump coupling. Fairly inexpensive. I don't think you need to replace the whole burner.

yes the bearing could be gong bad, the screws could be comming loose which could make it where out the motor faster, it should be attended to