Spanish,
I think you really need to consider what you are doing and why you are doing it. First, a manual penalty means you are on Googles radar and you are outside their terms of service in some way. If your decision is to get a new domain then what you should do is put the old one in the trash and forget it ever happened. You are starting from square one if you are smart IMO. Why? because if it is a penalty around linking and you redirect to a new domain, you are going to carry that wait to the next site. That doesn't mean that the penalty will show up on your new domain at point just because of the old, but there is no real value in the links so why risk it? There are just too many reasons not to try and save the old and move it to the new with redirects. BUT, is there a reason you would not simply address the penalty? Maybe it is cost as cleanup is expensive; if so, you weigh cost of cleanup versus cost of rebuild to all new site with new domain.
Second, an "algorithmic penalty" is something we say from time to time, but if you are using that as a line of thinking - "the algorithm has in some way penalized us" - you are then setting yourself up for further pain down the road IMO. With a site failing to rank because you have bad links, poor content, ads everywhere, I suggest you not look at it as a penalty. Look at is as: "What must we do in order to grow our site in value to our customer and in ranking against our competitors?" If you believe you have a "penalty" of sorts you are really saying things are not as good as they could be. Why not change things? If it is linking, disavow bad domains and links and move on. If it is Panda in your thinking, what can you do to change the content, etc.?
Often, when this type of question arises there have been a series of missteps by a site owner trying to shortcut really building a web property. If there were true short cuts without risk, I can tell you I would have found them or learned of them from people on various forums like Moz. I simply do not know of any.
Clean things up and move on or start over and move on. I think that is the only choice you face. I wish it were easier for all of us.
Best