Am I responsible for that my PhD adviser does not have any fund or grant and as a result it really limited my research? I'm a PhD student at my fifth semester in the US. From the beginning of my PhD program, I didn't have sponsored graduate research assistantship from NSF or NIH. I was just on my PhD adviser's startup grant for two semesters and after that I got a job in another department of our university. Right now, I don't take money from my PhD adviser for almost a year and half (so basically I'm a free PhD student for my adviser!). By the way I'm not the US citizen or permanent resident in order to apply for NSF or NIH funds directly by myself so my options regarding funding are really limited or even I would say I don't have any option to get a fund by myself.

As a result, I built my PhD research based on open source available softwares as well as data sets, which I found it initially just by my research without my PhD adviser help. Besides that we don't have any fund, also we don't collaborate with anyone which again limited our options. This relying on open source softwares and data sets is really limited my research, cause the amount of data that I could use for my research is limited to those open source datasets and I don't have access to any other datasets, which might be available in other research groups, because of the problems that I mentioned earlier. The type of data that I need for my PhD research is related to medical images, which is not available easily everywhere and as a result it's really hard to find it as a open source dataset (I was lucky that I found at least one open source dataset!).

Let's say, I processed all the currently open source available data out there and analyze them and answered my research questions. But the problem is: there are several people out there, which are famous people that they are emerged in the field that I'm working on for years and have a big project from NIH or NSF that give them an access to some private datasets that are 10 times bigger than mine. Of course this bigger datasets increase the accuracy of the model that we are trying to work on as my PhD project.

Recently, my PhD adviser compared my accomplishments to these research groups that are engaged in big projects from NIH and NSF for years and said: by using your current open source datasets, it's really hard to say something in this field. I think it's not a fair comparison. Even our recent results with smaller dataset size shows comparable and to some extent better performance than other available models out there. Also, we studied several aspects of our research questions, which did not even touched by other people. So my question is: Am I responsible for that my PhD adviser does not have any fund or grant and as a result it really limited my research? How can I deal with this situation?
In general, this is bad form on the part of the advisor and your committee (shouldn't be approving thesis topics that are not viable if funding is not available). As a PhD student, you are in training and potential stumbling blocks should be made clear to you. 

For example, for my PhD I worked in a lab where I wanted to do field work in another country, but my advisor didn't have funding for this. I decided to go ahead with this part of the project, partially using my own personal funds, as well as cobbling together several small research grants to cover these costs.

So I would recommend to you that you investigate research funds that might be available from your department, institution, scientific society, foundation, or other non-federal source. Funding begets funding and you absolutely have to be successful in getting grants to be a successful academic. 

Additionally, it seems odd that an advisor could take on a student with no funding in the lab. That would not be allowed in my department (biology sub-field at a private, R1 university). 

Finally, to your last question: I think you are correct and it is unreasonable to compare the contribution of a single graduate student with "famous" well-funded labs! The contribution to your field during your PhD can be modest- that's ok- but it has to be good science, so I would focus on how to make sure that you are doing the most rigorous and sound research with the resources you have available. And get to writing grant applications! Good luck.