Inspiron 1526 connects and then drops connection - wired and wireless

I have an Inspiron 1526 that has been working fine since it was new (several years ago).   Now, when I turn on or restart the laptop it will connect to the network (wireless or wired) and I can browse the internet or connect to other LAN devices for a couple of minutes, and then the connection will stop working. 

The wireless signal (when attempting wireless) will still show 5-bars, and the ethernet port (when wired) still shows activity, but I can't connect to any LAN devices or the internet after the first couple of minutes.

I have several other computers connected to the same router, and none of them have any issues.

I've updated the networking drivers without any success.

Since the same thing happens with wired and wireless connections, I'm stumped - I think they use different cards, though I'm not positive about this.

Thanks for your help!

Kelly Meade

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Inspiron 1526 with Broadcom 1390 wireless, Windows Vista with all updates.