If you want apple to help you on such an old computer you will need to pay for support.
The diagnostic file is therefore useless.. however the utility will give you a simple list of issues.. if any were found.
The file on the desktop can be junked.
There is another function buried in the diagnostic, and while Assistant gives you mostly generalised rubbish the Utilities is excellent and works really well..
Open the Wireless Diagnostic but do not continue. Go to the top menu..
So simply click on the utilities. Another window will open.
On the main screen then you can kill the Assistant Window.
With the utility go to Wi-Fi Scan.. therein lies info that is crucial to getting some idea what is going on..
Of course I am not running Yosemite.. which IMHO is barely past Alpha stage development. And therein is most of your problems.
Do the WiFi scan and see if your wireless is working at all.
Apps like Memory Clean can be 90% useless.. and load your computer with spamware.. spyware.. maybe not viruses but they pester you forever and ever more.
If you upgrade installed Yosemite onto a working computer and then started having issues.. you can pretty much guess where the problem is.
I have a long list of recommendations to fix it.. but perhaps it is best if you are finding this hard.. do a screenshot of the wifi scan and post to me.
If it fails then the issue is indeed Yosemite and we can work from there.
2GB is very short memory.. even in 2009 apple was hoping to extract more money from you with a memory upgrade.. you desperately need more RAM.
However it might be better to think about it.. a 2009 computer is well and truly due replacement. Buying old style memory (forced to replace the existing RAM) might cost you $100 (whatever that comes to in UK Pounds).. 8GB is kind of min these days. If the computer breaks down shortly after that will be a waste. And running it on Yosemite is a bad idea all round.
For now post your wifi scan screenshot and clean out all the current wireless names you have stored under the network preferences in wireless.. Advanced, WiFi, Preferred Network.. remove the lot.. then reboot the computer and do another search for the wireless when the computer comes up..
Reset the TC to factory might help.
Factory reset universal
Power off the TC.. ie pull the power cord or power off at the wall.. wait 10sec.. hold in the reset button.. be gentle.. power on again still holding in reset.. and keep holding it in for another 10sec. You may need some help as it is hard to both hold in reset and apply power. It will show success by rapidly blinking the front led. Release the reset.. and wait a couple of min for the TC to reset and come back with factory settings. If the front LED doesn’t blink rapidly you missed it and simply try again. The reset is fairly fragile in these.. press it so you feel it just click and no more.. I have seen people bend the lever or even break it. I use a toothpick as tool.
N.B. None of your files on the hard disk of the TC are deleted.. this simply clears out the router settings of the TC.
See if you can then get anywhere.