I know this is an old topic, but it's actually one that I had to go through today. Researching how to fix ssleay32.dll lead me to no where. I tried the sfc /scannow command in cmd prompt and returns no results/errors. I scanned my system for any viruses and it's clean. I checked the folders for the file and in fact the file was indeed available NOT missing. So something was throwing the game off to start. I remembered that in the same folder where you install Dragon Age II there is a configuration utility that lets you somewhat modify the settings the game uses for example the video, audio, and so forth. Very limited but I found the issue to be in there and tested it to confirm.
In my case I clicked on the shortcut the game installed on my desktop and [windows 7] I right clicked to give me options. I then clicked on Open File Location. In the folder double click on "DragonAge2Config" in doing so will open up the configuration utility. Look at the left column and click on "Video" [it's right under WELCOME]. Now on the list on the right side there is several options. The one that fixed it for me was near the end called "Renderer" which in my case by default set to "DirectX 11 (if available)" so when loading the game is trying to use the DirectX 11 which in my case my video card [laptop] doesn't support version 11. So in doing so it's causing issues loading the game.
What worked and I confirmed this by changing it back and forth and reloading the game to test it.
I changed "Renderer" to DirectX 9 then I clicked on the top area where it says "Dragon Age II" in between File and System. I then clicked "Save Dragon Age II Settings" closed it and then opened the game from the desktop.
In having it set to DirectX 9 the game loaded perfectly.
In changing or leaving it DirectX 11 (if available) it gave me the "ssleay32.dll missing" error.
I just wanted to report this even though it's an old topic but it's relevant and it will help other users to fixing a simple problem.
And yes I've done my research and I have yet to find a topic that shows this step. Had to find it myself.
Enjoy! and post if this worked for you.
Thank You and Enjoy the game it's actually really fun and interesting.