How do I record my own drum beats using SI Drum Kit in Sonar LE? I can copy over one of the pre-recorded patterns but I want to be able to lay down my own beat using the drum kits. Is there a way to do that? If so how? I've tried everything. I'm very new to all this and I'm eager to learn. Thanks.

You can simply edit the ready-made MIDI loop or draw your own in the same Piano Roll, or record one with a MIDI-keyboard or controller if you have one. You obviously haven't tried everything :o)

Welcome to the forum.
Kalle's right, you can't record the sounds from the onscreen drum set; that's just for auditioning the sounds.
you can enter MIDI notes in either the piano roll or staff views, or record your performance live with a MIDI keyboard or controller or drum machine that has pads you can hit.

Thanks for  your responses. Will any USB drum pad work with Sonar LE? I was thinking of getting the Akai MPD18. I would post a link but the site won't let me yet. I guess cause I'm new. LOL.
 
 

Any will do, AFAIK. It doesn't even need to be a drum pad. I record drums with my MIDI-keyboard.
If you don't have a MIDI-keyboard, which I think is the most necessary tool, you might consider one with pads??

For almost 30 years I entered my own drums by banging away on the C2/D2 and F#2 keys on a basic MIDI keyboard.  I would start with a looped pattern and then record the Bass part to make the arrangement. I would then go back and re do the drum parts to add the fills and half arsed fancy stuff. Still sounded like a drum machine but 100% better than a loop. I find working this way much faster that spending hours or even days entering data manually. 
Takes about an hour from scratch to 90% finished song. 
 
I tried drum pads and found no real difference from the keyboard, other than you can hit them with sticks. Most still would not record a true roll. also harder to control the velocity.  I now own a set of Digital drums and that is by far the best way to get a realistic midi part laid down.
 
It all depends on your own musical abilities. Being a guitar player it took a long time just to even start thinking like a drummer. 
They make some pretty cheap digital drum kits these days. 
But you will want a keyboard for inputing other midi instruments. So I would start there first.