How do I get out of my problem of not achieving results, feelings of worthlessness, guilt and rejection? I am currently a PhD student in a biomedical related field.
I came a long way. I first did my undergraduate and worked for a few years, though not research related. Later, I identified my research interest before embarking in the PhD with the hope of fulfilling my career dreams. I used to love and enjoy science, but that was long ago. I was happy when I got into the PhD program. Now I'm nearly 2 years into my study, mostly 'wet' lab and basic sciences research.  

Unfortunately, my experiments - most of them - fail. Initially, that was due to lack of skills and experience - with time things have improved but I am still lacking good results that can give clear direction in my work.
My project has been modified a few times because initially there were problems with the biological samples so I had no choice. Then, I tried to 'reproduce' a piece of result done by a colleague few years ago but the results were always 'off' no matter how many times I did it. Even someone else with better experience in the lab tried but could not replicate the same result. The conclusion was perhaps, change in phenotype of biological samples over time.
Then my project changed again, and the technique is now becoming more complicated and 'taxing'. Partly, because my supervisor is not very happy and feels that it is time I should be producing good data and should aim for higher impact. With more complicated experiments, I also need to beef up my basic sciences knowledge but as someone coming from a different background it is taking me extra time to grasp. With my confidence going in a downward spiral.  

I am finding more and more difficult to articulate my thoughts clearly to my peers and I feel constant 'rejection' and 'guilt'. Most of my colleagues are actually good people, but harsh words, although not ill-meaning, are slowly eroding my confidence. When I ask questions because there is something that I don't fully understand (without prior knowledge and not something I can read up on), people appear impatient and ask back (e.g. "why are you asking?",  "what do you think?", or just "I can't give an answer to you on this"). It feels more and more difficult for me to ask questions or speak up for myself.  

One day, I was blamed for something (from someone outside the lab) that I didn't even do. The accusation was pretty unreasonable - others who witnessed the event felt the same - but to me I felt I was just a bully target. I just broke down and cried because I realized I couldn't take the stress and frustration of rejections and failure.
My friend in the same lab gave me some counseling but also at the same time asked me whether working in this lab is truly what I want to do. I don't want to quit my PhD, but then again I don't know how I can get out of this situation.  


Should I change project?
But my PhD qualifying exam is coming up and I am having a massive problem with writing up a good proposal because of all the frustrations happening.  
Should I change to dry lab?
I am afraid of talking to my mentor because I don't know whether at my current mental state I'll just suddenly break down again. 


In summary, my resentment and contradictory statements that I receive:  


Ideology: To do a PhD, perseverance is more important than being smart.
Reality: You need to be smart. REALLY SMART. 
Ideology: There's not such thing as a stupid question. Ask if you don't understand.
Reality: Huh? Why do you even ask?
Should I change project?
  Should I change to dry lab?
  


A PhD can be extremely frustrating and discouraging.  Whatever you do, don't make a major decision while you are stressed and upset. Take a deep breath (and maybe a day off) and decide what you need to focus on.

Since you will be qualing soon, you likely need to spend a significant amount of time studying for that.  Passing your quals are important, and will likely give you a confidence boost.

Secondly, consider finding a social outlet.  Many grad departments have a weekly social meet-up at a bar.  Apart from meeting people that work in different labs, it is also quite likely you will meet other people who have gone through this issue, and will help you.