Applying for (externally-funded) postdoc position: how to follow-up after 1st email? I would like to get a postdoc fellowship grant that is addressed to a specific department (in a particular top-tier university). Now I just need to get a professor there to accept to host me. 

While I think that my chances of getting the funding are high, I've emailed a professor to ask whether I could work at his lab (with this funding), but got no response after an email a week ago. 

I do believe that I'm a good match for the lab and a good candidate to get the fellowship, so... should I call/email this professor to follow-up? Otherwise, is it fine to just email another professor (in the same department)?
There's not a lot of specificity in this question, so I'll raise a few issues that struck me as being relevant:


You seem to be more interested in joining the department rather than working with a particular professor. The way you're describing it, you've contacted one professor but are prepared to contact another should this not pan out, heading down the department's staff list until you get a hit. I'm not going to comment outright on this technique or motivation. However, if you wish to be efficient about this, why not contact the head of department and state your case: you've got a fully-funded post-doc fellowship and would like to work in such-and-such area?
Your assessment of the chances of getting funding are not absolute and there might be some hesitation in the mind of the professor about the benefits of receiving the grant money on the one hand and your track record, competence, work ethic or some other factor on the other. It's not only about the money. What downside are we (or you) not seeing?
Not all fellowship awards are created equal. Money from some sources are prohibited by some labs. For example, if you came to us with money from British-American Tobacco, we'd be ineligible to even apply for, let alone receive grant money from important sources in the future.
The lab may simply be full. That is to say, someone has made a decision to impose a hiring freeze for reasons other than money. In my previous university, this happened just before "restructuring" took place resulting in major job losses.
Sending out email and expecting a quick response at this time of the year is extremely dicey. In my area, people go on holidays and don't emerge until in January or February. This might be poor timing.
Do you have any networks that extend to this lab or department? It might be worth your while mining them to see whether someone who knows someone can link you. A friendly introduction from a mutual acquaintance is much more effective than a cold call.


Good luck.