However I don't have a weight set. I have two weights, with 4 ten pound weights (20 pounds for each weight, in other words.), a couple of tiny non adjustable 5 pound weights. Does anyone have any advice for advancement?
I've heard doing "diagonal pushups" is a good start, is that true, or did I just stumble on some fitness related nonsense?
If you can't do a pushup, then your best bet is to work your chest and triceps before attempting to do them. Unless you CAN do them, with enough effort, yet cannot muster it.
You'd be surprised how easy it is to do pushups once you get the right technique down. I go to bed on a set of 30, and I don't consider myself very strong (only bench about 260 these days, it was 300 in school :[).
But if you really can't, then your best choice is to use the light weights and do Chest Presses and plenty of Benching until you build the strength to do so. I bet you can do atleast one if you do it correct, though. It's basic human anatomy, unless you're severely overweight (like I used to be, until I was about 16). Curls CAN help, but my pushups don't utilize the bicep since I do them so close, so I think that's more of a glamour thing. Triceps are what really help you pop off the ground if you're getting exhausted.
Once you can do pushups yourself, then all it takes it some effort and time to boost your ability to do them. Do as many as you can in one setting, even if you max out at ~3 or so, it's still worth it if you feel it in your arms and muscles. Not everyone is a bodybuilder, so don't expect to become superman in a couple weeks. Just keep doing a few sets of pushups a day and you'll see improvement, slowly but surely. Then you can ramp up your intensity.
I typically try to do as many as I can before my right arm gives out on me, since it's my weaker arm. At the end of the day it's all about what makes you feel comfortable.