Postdoc application email with PI I came across an advertisement for a postdoc position at a US school. While I have a PhD from a (different) US school, currently I am in India (my home country). I had contacted the PI to check with her to see if visa support is available for this position. She replied saying that she will support my visa if the fit is right. She also gave me a small problem to work on and asked me to return my solutions in a week. I did. It's been two weeks since and I haven't heard anything back. 

While I realize that there could be any number of reasons for not replying (such as she's busy, or no longer interested or waiting for more people to apply), a simple reply confirming the receipt of my solutions would help.

If anybody has any ideas as to what to make of this situation, please do share.
As you say, there are numerous possible reasons you may not have heard back yet.  I have been on both sides of this equation, waiting for a response and waiting for all the applications or letters of interest to come in, and although two weeks is a long time for you, it is not excessive for the employer/PI.  

It is totally appropriate for you to politely contact this person and briefly reiterate your interest in the position, and say you want to be sure she received your answer/solution to the problem she posed.  This will also allow you to request information as to when to expect to hear back with a decision or next steps, and see if there is anything else she needs from you now. 

It would be best not to go into the details of your Visa situation again at this time.  She's already answered that question.  If she responds positively to you and requests further information or an interview, you will be able to discuss the Visa at that time.  You don't want to sound pushy or needy at this point, but you do want to be assured she received your response and knows of your interest.

Good luck, I wish you the best.