I have a 1020, have had it for 15, maybe 20 years, maybe more. Great machine. I agree with the above suggestions. Dirty fuel filter first. I replaced mine with one of the clear in line filters - I can see it any time I want to take a look.
I don't think this is your problem, but it might come in time - there is a solenoid for shutting the machine off - it stops the fuel from going into the carburetor. Mine gave me trouble and tried to fix it. No luck after several tries. I removed it and held the shut off needle open with part of a paper clip. Then I used a 35mm film container as a cap for covering the valve. It has been running that way for years.
No cranking at all is an electrical issue. You may have run the battery down completely. Get a charger on it as soon as possible. you may not have completely killed the battery.
Try jump starting it (without the charger in place). If you can, then the battery is down and the charging might fix it.
If the key does nothing, absolutely nothing, then you might have a broken wire somewhere. Use an air hose in the battery box (watch your eyes - dry dust and dry battery acid is a bad thing in the eyes). Blow out the box and start watching and wiggling wires - a broken one might come off in your fingers. Check to see if you have voltage going into the coil. If you have that you should have spark. Check spark as mentioned above.
You have a really good machine that will last for years with reasonable maintenance. In the big picture this is a very basic machine that is easy and pretty cheap to maintain. Thank your brother in law.
BTW - mine has a loader on it and it is incredibly useful. Model 48. They can be found and fitted to your JD.