I need help with identifying a mechanical device/part located next to the car engine?

I need help with a few things, the most answers you can provide would help me out enormously!

Car is a Honda Accord 2002 EX v6 Coupe 3.0L

Ok, So here is the deal. I will post up a couple of pictures of the part which is unknown to me but I do know it needs to be replaced or fixed. And also would like to ask what would be causing my 3rd gear to start slipping/revving. Note that I had my transmission replaced back in mid 2010. I'm thinking it has to do with the one of the pistons maybe? and well obviously within the transmission, but im trying to narrow it down a bit more. I dont know a whole lot about cars and I dont make much income as I care for my elderly father.

Mainly, Im just looking for help with identifying the problems the best you can with the information I have provided. And maybe to add some links to sites where I can do my own research on it. Anything at all will be helpful, if you want to take a guess at a price range too for all of it then please feel free to do so. Thank you all SOOOOOO MUCH!!!!!!!!!!!!!!!!!!!!!!

Very very very very appreciated!!!!! Hope you all enjoy the rest of your day!

Also, My car wont start because of this. Not the transmission, but the mechanical device in the pictures below.

 

Whatever advice you can give is soooooooo much appreciated thank you!!!!!!


If you need more pictures please lt me know and ill have them uploaded ASAP Ty Ty Ty SOO MUCH

 

Please please help, I need to get it fixed asap for a new job im starting in a couple days!!! I've posted this on a few forums but no one seems to have enough knowledge about this are. Either that or Im not giving enough information. PLEASE help, I will be so grateful!

 

Does your cruise control work?

 

The part you need to buy is called the "throttle shaft bell crank" its broken and not holding the cable in place

 

Thank you all so very much!!!! I was researching for hours, I just don't have a lot of money since I was laid off last year. But trying to get the car back on the road again. Can;t aford a mechanic so Im learning all I can to do the repairs myself.

One more thing, it seems that the 3rd gear gets stuck all the time well at least before I took it off the road. Not really slipping butn it seems like one of the pistons is not right, A brief explanation would be that when I switch into 3rd gear the engine starts revving like an example of someone showing off but this is while i am drive and it wont go past 60 mph.... Any ideas. Just had the Transmission replaced a couple years ago =(

BTW, I just wanted to let you guys know that you are all awesome and very helpful!!!!!! I appreciate your help greatly!!!!!

 

And no my cruise control has not worked for a long long time.