Mercury trouble - please advise

[Chelsea FC]

Here is sequence of events from last 2 days. Mercury 2004 50hp

Going in I knew my cranking battery was weak, but boat started up fine.
-Made a 5min run no problem and fished for hour
-When I tried to start it, I had nothing and voltage was little low. Could only hear a clicking
-Voltage gauge was working, but just seemed like battery might have finally bit it
- Jumped off from a friend's boat
- When I tried to go it would not go on plane. Only 3500rpm going fwd
- Got it home and replaced battery to eliminate that problem
- Went to crank it in backyard (motor in trash can) and had nothing!
- Started reading up on stuff and played with the gear shift .
- I actually put it in gear one time and turned key a little and it made a noise
- back to neutral and it started up
- Checked it many times over the next 24hrs and it started right up every time
- cleaned fuel filter
- back on lake today, starts right up but still only 3500 rpm in FWD

I noticed that RPMs will go full power when going reverse but only 3500rpm when fwd.

Friend said hub might be slipping so we made a mark on hub and prop but after 5minutes of running they are still in same place

any advice at all?

[Chelsea FC]

something in the throttle box ?

[EuropeanAM]

Inspect the voltage regulator for signs of burnt spots, browned-blackened-melted connectors, etc.

Verify battery via a LOAD TEST. Ensure battery cable connections are CLEAN, engine cable installed FIRST, remaining lugs Largest to Smallest, and finish off the connection with a Stainless Locknut (do NOT use wing nuts).

[Chelsea FC]

thanks Euro. Will check when I get home. Had voltage regulator replaced last year and engine doesn't get a ton of use.

battery is connected like you directed.