Usually ligands are not accepted by servers only protein molecule is considered. I would be interested in simulation of protein along with the ligand or ligands.
You do not need server (free online), if you use MD. You can download some of the free of charge packages (https://en.wikipedia.org/wiki/Category:Molecular_dynamics_software) and to run computations in your personal computer. Depending on the theoretical level and thepower of your machine you can compute about 20 000 atoms (even more) in a single run.
Then these systems/properties, which you have found as most important ones to your study you can compute at an increased accuracy in the server of your Institution.
In particular, only ligands you can run in your personal computer even at a high accuracy using ab initio methods.
Unfortunately, there is NO online server that a person can use. Generally, you have or your university has to purchase such one. The prices for such servers dependent on the memory of the server. However, as Drago mentioned in his answer, you can download one of the listed programs and run your calculations with.
You do not need server (free online), if you use MD. You can download some of the free of charge packages (https://en.wikipedia.org/wiki/Category:Molecular_dynamics_software) and to run computations in your personal computer. Depending on the theoretical level and thepower of your machine you can compute about 20 000 atoms (even more) in a single run.
Then these systems/properties, which you have found as most important ones to your study you can compute at an increased accuracy in the server of your Institution.
In particular, only ligands you can run in your personal computer even at a high accuracy using ab initio methods.
(Sorry, in my previous post, I must have overlooked the important keyword "molecular dynamics" via my mobile phone while on travel. Having a second look at this page on my desktop did I realize that I have not answered your question. Here is my second attempt.)
So you would like to perform MD online, in addition to the GROMACS web server suggested by Natalia, I would also recommend the following free server (requires registration):
1) MDWeb (see Link 1). This server supports MD of protein-ligand complex. Tutorial on using MDWeb is also provided on the website (see Link 2).
2) HADDOCK (see Link 3). HADDOCK is also hosted on the same server as GROMACS webserver mentioned above on the WeNMR infrastructure. HADDOCK supports a wide range of docking possibilities: protein-protein, protein-nucleic acids and protein-ligand complexes. An overview of the HADDOCK server is provided in a recent article published in Journal of Molecular Biology (see Link 4). Tutorial is also available on their website (see Link 5), on YouTube (see Links 6 and 7). A Nature Protocols on how to use HADDOCK is also available (Link 8).
In your comment you have mentioned that "Depending on the theoretical level and the power of your machine you can compute about 20 000 atoms (even more) in a single run". Could you please recommend some ab initio MD and DFT codes which can handle such a large number of atoms on a simple laptop (core i5 or i7)?