My laptop...doesn't do this. First, it doesn't last very long in "suspend" mode (it has to power all of its RAM and the battery only lasts so long), so it ends up "hiberating" after awhile. This makes opening the cover take 20 seconds. After that, it has a tough time finding its preferred wireless network and getting an IP address from DHCP (altogether ten more seconds), and this makes it almost faster to walk into the next room and use a desktop PC.
The PC industry has been talking about this problem since the introduction of the Mac in 1984. And now I can actually buy a big chunk of Flash disk to wake my computer up faster.
But after the hardware problems, the software layer is still not built for this -- getting "on" the network (and reconnecting to IM services, email, ajax apps, etc.) is also too slow.
In addition to improving wireless/DHCP, we could a lot better with desktop APIs. Today the Windows OS doesn't give good signals about "why you're not connected to the Internet". It could be a proxy server, or T-Mobile wanting you to login, or just "I don't have a network address yet".
If you write software, you get a message like "Something broke. Sorry." You can't ask again really fast, because it might actually be a server that you're talking to (an overloaded proxy or your own production box). So you end up waiting a while, and then trying again. This means that on average, applications will take 30 seconds or more to wake up after you have a real network connection. Yes, you'll say, Windows has some of these APIs, but they very simply don't work. They'll pick the wrong network adapter or just give wrong information. And so everyone ends up being careful instead. And you end up waiting another 30 seconds.
Even if there were a single service on each PC that did this really really well, and other apps could ask it, "Hey, is there internet yet?" that would be a huge improvement.
Until this kind of thing gets addressed, the PC is going to lag the mobile phone for a whole lot of applications. That's pretty sad, because a few smart people could fix it pretty fast.