SUMMARY
The poor engine running with a 2005 Mercury 115-HP FOURSTROKE was due to fuel starvation caused by obstruction of fuel flow at an in-line filter under the cowling.
THE PROBLEM AND ATTEMPTED REMEDIES BY MECHANIC
On my first use of the boat, the engine ran roughly and seemed to lose power. I took the boat to a local shop. The "fuel injection" was cleaned and the fuel filter was changed. I used the boat again, but there was no change in how the engine ran.
[With the boat back at the local shop] the mechanic measured the fuel pressure and described the measured pressure as "very low." The mechanic surmised the fuel pump in the vapor-separator tank assembly (VST) was bad. The mechanic stated an estimated repair would require four hours of labor and replacement of the pump in the VST. Upon attempting to order OEM parts, after a week's delay the mechanic told me the necessary parts are now obsolete.
FIXING THE PROBLEM MYSELF
With little faith in the mechanic, next I tried to fix the problem myself. I took three initial steps toward a solution:
- I used a portable tank (so as to eliminate the possibility of bad fuel in the main tank being the cause of the poor engine running);
- I changed the fuel line and the primer bulb;
- next, I "opened up" the engine, l got to the VST, I tested the pump on a bench, and I changed the filter [a filter in the VST perhaps], which took half a day and was my first experience at this sort of work, and required removal of the [lower cowling or midsection in order to gain access to a fastener needed to remove the "silencer", the engine block, and the VST;[/list]
I then saw the filter in the VST was about 40-percent "clogged up." This was a disappointment because my hope was to find the filter "clogged up" to 90-percent--or something. I then knew [the 40-percent "clogged up" filter] was not [the cause of the engine running problem].
The engine [was put back to running condition and the boat was tested again]. {The engine continued to] run roughly at idle speed and appeared to be starved for fuel when shifted into gear.
Knowing that the [fundamental cause of the engine poor running was due to starvation of gasoline] I began a process of elimination [to find the cause of the starvation] by [using a method of testing that would] eliminate one [component of the fuel system] at a time.
[The first component of the fuel system I tested in my process of elimination was] the low-pressure fuel pump. I inspected the low-pressure fuel pump.
[The second component of the fuel system I tested in my process of elimination was a hose and primer bulb.] I opened a hose and squeezed the primer bulb: fuel came out "good" without any leak.
Next I made this observation: [downstream] of the low-pressure pump is a "looking-big" fuel line with a heat shield cover, [which I will describe as] the in-line fuel filter [strainer or filter]. Again, I removed a hose and squeezed the primer bulb. Only "a little" fuel came out. I then knew I had found [the cause] of the problem [of fuel starvation in the engine fuel system].
UPDATE TO PRESENT DAY
I bought a non-OEM replacement made by Sierra on Amazon that had fast shipping, I tested the boat. [The problem of poor engine running due to fuel starvation has been remedied, and] the engine [now] runs "like a dream."
I also have ordered the OEM part [and I am waiting] for delivery.

Fig 1: the 2005 Mercury 115 FOURSTROKE engine with cowling and other components removed.

Fig. 2. The partially 'clogged up" filter in the [high-pressure] pump.

Fig 3. The 98-percent "clogged up" in-line fuel filter [or strainer].

Fig. 4. Testing with the new in-line fuel filter [or strainer].