I would first verify you have a good IP address assigned to your PC. Open a MSDOS prompt window and type in "ipconfig" without the quotes to verify the IP address and gateway address you have. Then try to ping the gateway at the command prompt, key in "ping xxx.xxx.xxx.xxx" without the quotes where the xxx are what was displayed from the ipconfig. You can also key in "ipconfig /all" and insure you have a DNS address configured. You did not say how your hotel has their wireless network setup, but most I have seen require some form of initial configuration before you are allowed to go out of the local network. It appears that your problem may be in this area. If you can successfully ping the IP addresses, then try to ping an internet address like "ping microsoft.com" and verify these also do not time out. Post back results of the ipconfig and ping attempts if you still have problems, and hopefully someone can jump in to let you know if this is okay. I would not believe your battery is the cause of your problems.
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