Fragos, I think you are having different problems. I can ping perfectly to and from my N800 and all network PC's by using their IP addresses. No loss whatsoever. My problem is that I can't use the defined network names...

I've had to manually add them to my hosts file. not ideal; but it works.

as root, run
vi /etc/hosts
add a line like this:
10.0.0.131 htpc

Yeah, I understand that is a work-around... But I would prefer to understand why the name lookups all fail...

Is there anybody who can explain to me this stuff about local DNS and domains?

Are you sure it's your router that's providing a local DNS server, or are your Windows XP machines doing some other kind of name resolution?

My TRENnet router responds to my PC's DCHP request with the routers IP as DNS. Apparently it forwards my DNS requests to my ISP's DNS servers because they still work. If I look at my router admin it shows the ISP's DNS IP's.

I haven't put up / configured any DNS, not in the router and not on any of the networked PC's. Just given all the Windows PCs a network name when configuring their network settings. However, my Linux-based Linksys WRT54GL displays a nice list of the names and their respective IP addresses.

Is there any additional software I need to install or configure to get this working on the N800?

For an experiment you should try turning of WiFi power saving. This will dgrade your battery life but may be required depending on how well your router implements power saving protocol. Even well implemented there are situations where another PC initiates an action over WiFi which may be missed by the tablet and assumed an error by the requestor. This tends not to be an issue for actions initiated by the tablet out to the Internet over a router which properly implemented WiFi power saving. Turn power saving off on the tablet and if things work you have the problem. This parameter is by connection and won't impact routers with other SSID's.

Haaaa..... That worked !!!!

I turned off power saving, and now I can ping by hostname. And the weird thing is, even when I turn power saving back on, it still works. Even after a reboot of the device. Is this because some bit of information needed to be downloaded from somewhere, and that didn't succeed with powersaving on? Anyway, I will keep a close eye on this, see if it continues to function.

Is turning powersaving off a common solution for networking problems? If so, then maybe this should be indicated somewhere, for example in the wiki or a sticky thread. I can't believe that I would be the only one having this problem?

Anyway, thanks very much!

If your use of the tablet was only to access the WAN at host spots and home chances are you won't see this problem. Equal participation on a LAN interacting with other LAN devices that initiate transactions with the tablet you will see this issue. Many applications on the LAN assume an instant allways on link and haven't accomodated WiFi power saving. From what I see ping is a good example. I don't have a detailed understanding of the power saving protocol but it appears that it's design may have assummed the purpose was Internet access and that only the device with power saving and the access point it connected to would be aware of power saving. This is all based on observation so there may be some flaws in my assumptions.