Addition of third computer in network causes router to drop internet connection (is the problem Dropbox???)

Hold down the Option key while you click on the WiFi Icon in the menuBar, and report the stuff you get like this:

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also, how many other Routers (from your neighbors) do you see?

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You seem to have very good signal strength, although that display does not show the impact of noise and interference.

If you only ever see one neighbor, that is not a lot of competition from nearby networks. Actually joining neighbors' networks is not what I was fishing for. There are only three effective channels (1, 6, and 11) in the 2.4GHz band your Router supports. Their being visible means they are using up the limited number of clear channels available. If you could see three or more others, even occasionally, that would be a big problem.

Your overall speed at this Mac is only 54Mbps. But that is likely faster than your Internet connection speed, so it should not be a bottleneck.

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If you were interested in updating to a more modern Router, Apple's newest 802.11ac dual channel Airport express is very nice. I bought mine as an Apple factory refurb (pristine condition, same warranty as new, but cheaper).

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It is possible that the high data requirements of multiple Dropbox connections along with other the connections are beating on your Router and the concentrated data transfers eventually overwhelm the Router. But there does not seem to be a known vulnerability inherent in DropBox connections.

Also, there are no other networks we pick up here. Sometimes, we randomly get the neighbor's, but it's protected and we don't ever join it.

Try the basics first:

Change your router channel number. Most times this works & is all you have to do.

Disconnect & reconnect your modem. unplug it for about 10 seconds. Plug it back in. Do the same for Apple’s routers. Wait for everything to reboot.

System Preferences>Network

Click the Assist Me button.

In the next window that pops up, click the Diagnostic button & do the necessary.

Research Knowledge Base for network problems that pertain to the OS that is currently installed on your computer. See these basic networking KB Articles: http://support.apple.com/kb/HT1401 AirPort troubleshooting guide

http://support.apple.com/kb/HT4628
Wi-Fi: How to troubleshoot Wi-Fi connectivity

http://support.apple.com/kb/HT2712 Using network locations in Mac OS X

Manually provided DNS server addresses are higher priority than DHCP's

http://support.apple.com/kb/HT1714 Solutions for connecting to the Internet, setting up a small network, and troubleshooting

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What to do when you can't connect to the Internet

Also, run the Airport Utility app which is located inside the Utilities folder.

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If using a Linksys router, contact LinkSys Customer Support and/or post in their forums.

If using Apple's Airport, please re-post over in one of the AirPort Forums.

Gigabit Ethernet provides "near Hard drive" speeds, theoretically up to 125MBytes/sec, about the top speed of typical Rotating Hard drives.

I am seeing much faster WiFi speeds with my new Apple Base Station -- nearly five times your nominal speed (look back at the sample report I posted above). And the three User Ethernet ports on it are Gigabit-capable for fast computer-to-computer transfers without adding an additional Switch right away.

jsml wrote:

I really think it's a bandwidth issue that is overloading the network, whether it be a file access/transfer or two Dropboxes trying to update at the same time.

I don't think so. A good modern router should be able to handle several Gigabit streams, which is a whole lot more than you could generate from a couple people accessing Dropbox, since almost no one can get Gigabit speed Internet service. And if a good router somehow did hit whatever limit it is capable of, it should not restart. It should just keep going, just limited by its capacity. And when that happens most users should not even notice, since that limit should be faster than the Internet speeds most people are used to.

One demonstrated torture test is the common scenario of a mom-and-pop coffee shop with a consumer router (and I've seen a lot of basic Linksys routers in coffee shops). The coffee shop owner has absolutely no idea what brand of device will walk in the door or how many. Yet every day hundreds of coffee shops across the nation have a lot of users with often a couple of devices each (laptop and phone) piling on to the wifi, many of them downloading videos or other large files simultaneously, or a lot of students and freelancers with their Dropboxes updating constantly, yet the consumer router does not break. That is how it's supposed to work.

If a router isn't able to hold up under a much lower load than that, one thing I would do is go to the router maker's web site (in your case Linksys) and see if there are any firmware updates for the router. If the restart problem is known, they might have a fix for it.