I've heard Gamemaker is good because you can start off without needing to code at all. Then as you get more comfortable with the concepts you can start to learn how to code through it's scripting language.
which I've heard is similar to Gamemaker but works with Actionscript 3 the language of Flash under the hood.
There's also Scirra Construct
which has a new version under development and looks very promising as well. It'll export to HTML5 which should let you reach a lot of different platforms.
I think with any of these engines you can get off the ground without having to know how to program at all.
As for myself I've been re-learning how to program first before tackling any game projects. I was interested in programming and studied it in college long ago but much has changed (and I forgot a lot) since then. So far it's been a uphill battle and not nearly as immediately rewarding as creating art though I think that it will be worth the effort in the end.
There are many free resources available to learn how to program. Here is the one I ended up doing over the last few months and recommend:
(copy/pasted a bit from another thread)
You can learn the fundamentals of computer science and programming here
, course materials here
, free pre-press version of the textbook here
, and the other textbook here
, at the course website