Since you're new I'm assuming you don't know all your options - monkey wrench racing is not too far away and has engine options for you. As long as you're not straying too far off the beaten path I think its a good option, I know someone who bought one of their engines last year and things are still going well

 

Used with options

Toyota 2ZZ-GE Engine (Long Block) - Used 20-60k (No Air Injection)

Built engines

Complete Built Engines

 

You missed hitting WTB before posting despite the warning in the instructions. You have a FS tag. Click on the three dots, edit, WTB, post.

 

Assuming you're getting the BRG Elise? Let us know how that ends up going!

 

I'd possess and test that car before committing to a replacement engine. That ticking sound could be something easy to fix. If I didn't already have a mini project I'd be very tempted.

 

Totally agree, it's a risk and everything costs more than you expect. But the engine starts and runs. That means a whole lot of things are working. Given the reported source of the damage I wonder if it may just be a chewed-on something that is touching an external, rotating part.

 

So this is has been a total misunderstanding and apologies to op. OP is coincidentally another 06 Elise without an engine, but out in Chicago. So jumped the gun there.
For that one, the listing says the car stopped turning over after that video so it does seem to be more of an issue

 

OK, maybe I'm the confused one. I'm referring to the green Elise listed here by @skylineguy26. I thought that @prvtdncr might be considering that car and planning on an engine swap. skylineguy26 provided a video of the running engine. Sorry for any confusion.

 

For what it’s worth my car is still for sale and I don’t have a completed deal with anyone.
glw finding an engine