My download speed is abysmally slow?

Call your internet provider. They may need to reset the connection you're getting.

However if you don't have a password on your Wi-Fi, that could also be the issue. If you're not password protected, the people around you could also be using your internet, thus slowing the speed

If you are connected by Wi-Fi, try measuring the speed using http://speedtest.net/...edtest.net using a computer connected to the router by Ethernet. If this shows a good speed, then the problem is your Wi-Fi network, which is your responsibility and not the responsibility of your ISP.

Try changing the channel the router is using. Try measuring the speed with other wireless devices.

Make sure that you are using the correct units. If you are downloading a file, then the speed is probably reported in Megabytes/second (MBps). If you multiply this by 10 you will get the approximate Megabits/second figure (Mbps), which is what speedtest.net reports. Note: mbps as you used in your question is millibits/second, and is fairly meaningless for Internet speeds. 1 Mbps = a billion mbps.

If you are downloading files, rather than running speed tests, remember that the site you are downloading from may only be supplying the data slowly.

If you get slow results with speedtest.net, then that is the time to call your ISP.

If your Lenovo is 802.11G then the most you CAN get is part of 54mbs due to the Wi-Fi card. Once you take off for Wi-Fi overhead you will see around 35-40 mbs at the most for that device!
Most 11G devices do run around the speeds you are saying you are getting. Either upgrade to 802.11N (inside the Lenovo) and in your router, or connect by etherent! When testing speeds, always use ethernet as Wi-Fi will not be close!

Call you internet service provider make sure all cables plugged in the modem.