1. Internet Service Provider (ISP). Since laptop maintains internet connectivity when directly cabled to modem, it appears your ISP is not to blame for your loss of connectivity. The issue of "throughput" is a separate issue which I'm going to ignore for now.
2. Modem. Sounds like your modem is operating properly because you maintain internet connectivity when laptop is directly cabled to modem.
3. Linksys Wireless Router. Suspect, very suspect. Currently you can't maintain internet connectivity with any of your computers for more than a few minutes using the wireless component of the router. Either "bad" overall hardware router, "bad" wireless subcomponent, buggy firmware, overheating, wireless frequency interference (neighbors, microwave, wireless phones), misconfiguration of router settings or laptop.
Per Broni's suggestion, you should attempt to maintain internet connectivity with computer directly cabled to one of the router ports. I'd start with a single computer. I believe you use "straight" (as opposed to "crossover") ethernet cable for this.
If this fails, you may have a bad router overall. To further test, I'd hardware reset the router settings back to the factory defaults, turn off the wireless component, and retest with single computer directly cabled to router.
How do you do this? You post the Model Number and Hardware Version of your router and you and/or someone else goes to manufacturer's site to get documentation and view forums regarding any hardware issues (reliability) with that Model/Version. There may also be "newer" firmware available for download, but I'd wait on that. You don't want to be the first to test drive their firmware. See what other users say about the reliability/stability of new firmware.
4. Model and Hardware Version. On my Linksys wireless router, there's a sticker on the bottom that says: Model No WRT54G v5 where "WRT54G" is the model number and "v5" is the hardware version. The hardware version number identifies a hardware redesign, not necessarily for the better.
5. Laptops. Assuming your laptops/operating systems are OK. Possible network configuration issue, but I doubt it.