Which leads did you order? Link? They don't look like they are necessarily junk, but maybe that is an issue for later. It looks like you have an actual XY pattern going on there, but something is off. What are those cables connected to on the other end?
The good news is you will know a lot more about oscilloscopes by the time we're done here. The bad news is I think your scope is a beaten, cobbled wreck that is going to fight us all the way to the end. No matter, I've fixed worse. Sometimes I think the most important quality in a repair tech is sheer stubbornness.
So, if you start with the dot on the left, nothing connected, put it in the non-XY normal mode (button out, right?) and set the timebase to 0.1S/Div, all 4 pushbuttons out, CH1 to 10mv/DIV with DC coupling, and the trigger centered and pushed in, what does it do? And if you give it an input with your DMM in ohms just like the test before, does it trigger? (Does the dot move horizontally at all?) If not, how about if you select trigger coupling "LINE"?
If not, then there's two separate things needed to track this down.
First, the inputs. Something is not right. It looks like the polarity is inverted from what I was expecting, but that alone shouldn't be a serious problem. Still, take the one you're using as the source (the Aneng I presume) and connect it directly to the other DMM, pos-to-pos, neg-to-neg and test the output voltage of the ohms function, including whether or not it is a negative reading. Then continuity-check your BNC cable to make sure you know which clip is connected to the center pin of the BNC connector. I want you to make sure in future tests that the positive source voltage is connected to the center pin--and if your voltage was negative in the first step, that means the negative lead of the DMM. Then, can you verify that when connected like this to the scope, the DMM reads approximately 1Megohm when connected to either channel?
Second, it looks like we are getting some signal through to Q808, but I've no idea what the actual signal level should be. So go back to XY mode, set the dot in the center to start and do the same measurements as the last step of last time, only on Q809 and at the base, emitter and the other side of R836. Don't worry about R832 unless it is super easy to get to. Then we'll compare the voltage swing at the base that it takes for Q809 to deflect the dot all the way from one side to the other to see if the 5-volt or so swing we had at Q808 should be enough to see(in which case Q808 is bad) or if the signal needs to be a lot more (in which case the horizontal final amp is fixed and we move on...).