***"Not to mention that I couldn't even find a owner's manual online!"***
Surely you jest.
Click the link below. When the Briggs site opens, go about 1/2 way down the page and find the large magnifying glass. To the right of that is a line requesting you to "Enter engine model number".
Type in the model number like this: 28V707-1113-E1 and then click the small black & white magnifying glass icon to the right end of the line. Next you will be presented with a list of choices for manuals. Choose the first 2 (IPL, and owners manual). You may have to do each manual selection as a separate operation.
When the manual downloads, save a copy to your computer and then do the same for the second one.
You can e-mail me for a copy of a service manual that will cover a bunch of Briggs engines, including yours.
But I can tell you that Briggs engines showing symptoms of the infamous KLUNKS SYNDROME are not good candidates for repair, even by seasoned professionals. Engine replacement is a more viable route.
My best guess is the previous owner ran it low of oil. The piston seized to the cylinder walls and caused the connecting rod to break.....OR.....the connecting rod seized to the crankshaft......causing the connecting rod to break.
So you are probably going to find a bunch of little broken pieces of metal, along with a few big broken pieces of metal.

Here is a link that might be useful: This jest in!

Thanks! I was hoping I won't have to replace the engine! If buying new parts, what is the minimum I will need to buy: engine block with piston.... is there a part number for the kit?
The other option is to look for a used engine.How do I make sure it doesn't have the same problem? :-) Should I be able to turn the flywheel or the pulley ( under motor) by hand, and make sure not to hear any KLUNK? Will that be enough? Please let me know.

Thanks again!

Wait until you get the service manual. (still waiting on your e-mail) and take this engine apart to survey the damage.
Used engines are sort of a guessing game but you definitely want to make sure you can turn the engine and hear no KLUNK, and that you can feel reasonable compression.
And always check that nothing is broken off of the engine castings, like where the mounting bolts go. Other than that, it's kinda like playing the lotto.

I sent you the email. I am not sure where you are, but what is the best place to buy parts and tools for small engines? For instance , I understand I will need the 19203 Briggs & Stratton Flywheel Puller (see link). The part is about $10 but if you order it online it will end up being over $20... Lowes and HD don't seem to carry it either...

Thanks again!

Here is a link that might be useful: 19203 Briggs & Stratton Flywheel Puller

Well, you don't have to get the flywheel off to inspect the guts of the engine. The sump cover on the opposite end from the flywheel can be removed with the flywheel still on the crankshaft. That is what I would do before going to the trouble of taking off the flywheel when you don't even know what's happened inside the engine.
You can buy a decent steering wheel puller kit at discount parts houses or tool stores that will do the job as well as the Briggs tool if it is necessary to remove flywheel later.

Thanks for the suggestion. I assume the SUMP COVER is the part the spark plug gets mounted on... ;-)

About the engine replacement: looking at the B&S site, under DIRECT REPlACEMENT option, there is only one engine ( under the vertical shaft engines list) that I could identify as being close to mine: 12.5hp (Model Series 219800 Power Built� - 12.5 Gross HP/344cc ) - luckily there was only one 12.5hp engine listed! Shoudl I assume it's mine? Am I correct? If not, how do I identify my engine and further on, how will I know I found the right engine if all I will have out there is the label on the engine ( like the one I put in the subject of my post) ?

Thanks again!

Here is a link that might be useful: B&S vertical shaft service replacement

I just looked at all the info I have about the engine and I am curious if B&S is using the engine code (instead of the model) in the DIRECT Replacement Catalog ? I am asking because my previous assumptions turned out to be wrong!

Here is my engine info:
model no 405002X8A
motor: 28V707
MOTOR TYPE: 1113-E1
CODE: 02050970

I couldn't find my engine model or code in the catalog!

Is the engine code being used in the catalog, in a format like 2050970?
Or should I look for model no: 286700 ( that's what you suggested to use). Which one should I use? Please let me know.

Thanks!

Got the message! Thanks for explaining it ! I loosened the 4 bolts holding the engine to the chassis but I think the pulley will give me a hard time. The screw that holds it ( look from under the mower, up) - is it a standard hex head type? It didn't look like a hex head ? I'll try it again tomorrow . Do you happen to know it's size (M or Inch).
Anyway, it looks I will need that steering wheel puller for removing the STACK PULLEY ASSEMBLY ! :-) NO matter which engine end I begin with, I still need it! See link below.

Thanks!

Here is a link that might be useful: Pulley removal

A puller can easily damage these pulleys if they hold their ground at all. 5/8" socket will do with an impact wrench or holding it securely w/ a pump pliers. 21B9070026 is what is shown as a replacement engine- which is strange. The dimensions are different than a 28 series and shows that it may need the harness reworked.

Steering wheel puller works well on the FLYWHEEL. But as tomplum stated, you might damage the belt pulley if it is stuck to the crankshaft.
Pay attention and look for one or more "set screws" located in the thick tubular portion of the pulley. If there are any set screws, remove them completely and spray your favorite rust bust agent generously into the screw holes.