Most new engines will turn over with drag but can be turned with a wrench.  If your engine is in the boat it would have to be turned using the harmonic balancer bolts on the front of the crankshaft.  Most engines will turn over with about 18-22 ft pounds pressure if using a torque wrench.   This is assuming your issue is mechanical.  If a piston is hitting the spark plug the plug gap will be bent closed or you will see some contact damage to the plugs.   

Maybe you just have a bad connection in your wires, with no plugs in it turns over because there is much less load / no compression, install the plugs and it is demanding an amp load that bad wires, connections or battery can't deliver.  

The other possibility I am thinking of, maybe you have hydro lock.  Water or fuel is entering the chamber and when the piston comes up it hydro locks.  Could be coolant getting past the head gasket or gasoline flooding from the carburetor.   With plugs out that fluid. would just drain out a spark plug hole, plugs in it locks up?    

Warning, if this is a flat tappet/lifter engine do not keep cranking the starter motor with no start.  Cranking alone if extensive can make a new cam go flat.  The engine must start and run at 2,000 RPM for 20 minutes right away to break in a cam.   IF you are in doubt Pay someone to come help before the cam is wrecked it will save you a lot of money and time.  If it has a roller lifter cam in it you can ignore this statement.

Good Luck, hope it is a simple fix.

I do not know your experience level so no idea if we are speaking and understanding.

If it turns over with no plugs but will not turn with plugs your distributor is not causing a mechanical lock up.

Timing is important.   If the timing is wrong it is possible to have fuel air and compression trying to explode in the cylinders well before the piston hits Top Dead Center and it can try to blow the piston back down, if they are all way off you might have lock up but it would turn fine by hand.   Or plugs installed remove the coil wire, that takes timing out of the equation.  If it still turns hard there is a mechanical issue, if it turns freely, while fighting compression as each cylinder hits TDC your issue is timing, spark plug fire order or both.

A new engine can be turned into junk quickly by a poor start up procedure.   It needs to be timed correctly, have fuel available and you want it to start on the first or second crank to properly break in the cam.  Not something to guess with or it will cost lots to fix it.   

I really hope you find some silly easy thing and it fires right up.

Maybe go back to the engine builder for help/advice?   If not most Shops with an engine Dyno have operators that know how to check tune and can do it quickly.

Example:  ARP oil pump primer tel:150-8801" rel="nofollow - 150-8801 .

Use a drill to the run the oil pump prior to starting.  Keeps everything nice and lubed up to avoid a dry start.  Do a search on YouTube and you will find lots of good videos showing you how to do this.  

https://www.youtube.com/watch?v=kvcq5BzBAZE" rel="nofollow - https://www.youtube.com/watch?v=kvcq5BzBAZE

JQ

I had to carefully adjust them with the intake open-do exhaust. Exhaust closing-do intake method. 

(there were several other challenges probably not applicable here...)

All Battery manufacturers advise you to fully charge the brand new battery before use.   Sometimes the battery will sit on a shelf before it sells for many months.  They discharge slowly while sitting on the shelf.   Many batteries today are built outside this country, they may be on a boat for Weeks before arriving in the USA and weeks more before you buy it at your local source.

If that is your only problem you are in great shape.

Not really knowing what you've used for a timing set, there's a chance that the backside of your cam gear may be rubbing on the camshaft retainer plate/bolts. There were variations over the years with different types of chain and gear sets. (Roller chain vs silent chain)

It can happen and that would produce lots of extra drag when turning things over by hand or with the starter.

A check of my memory banks seems to tell me that I had this problem once upon a time, but got lucky and found it before buttoning up the timing cover. 

It's kinda a sneaky gotcha when tightening things up 

Not really what you want to hear, but I'd probably take the timing cover off, then take the chain and gears off to check for "self machining" rub marks on the backside of the cam gear.

It's worth a look if everything else has you stumped

Also I checked how much force it took to rotate a good running fully assembled 351W engine by hand. It was in the boat, plugs installed and it took about 50 ft lbs to make it rotate.

I checked another engine too with the same results

Not the best assumption............ Ford still uses a timing chain on a RR 351w  

Umm......I think I knew that 

I was giving him an idea what it takes to get it turning with the plugs in since he mentioned that it took "a great deal of force"