Wireless seems real slow

looks like ou need to replace the ram card

you can go on Free-PC-Cleaner.sparktrust.comClean PC, Boost Speed, Fix Errors and download it and ican assure you it will work.
if that does not work go on www.speedtest.net.

Please refer to the following article for some tips on how to troubleshoot wireless connectivity issues:
http://www.fixya.com/support/r6556655-troubleshooting_laptop_wifi_connectivity

You might have an extremely slow boot up. Try tapping F8 the next time you boot to start up in Safe Mode. If Safe Mode boots up faster then you should try removing some of the Startup items that you find when you run msconfig from the Run box.

its the button on the left-next to the power button-is the wireles icon in blue on it-cantb be missed

According to the spec sheet, at this link Yes.

Wireless support4 category:
Intel 802.11a/b/g/draft-n, a/b/g, b/g, Broadcom 802.11a/b/g, b/g, Bluetooth™ 2.0, HP Wireless Assistant

Looks like memory issue, Try another OS and see, You can download and install 30day trial from www.microsoft.com

The wireless button is also the indicator light to the left of the power button. This confused me for a while too!

Here the average price in US$

HP Compaq Business Notebook 6720s - Celeron 2 ...

$401 to $766 - 8 stores

HP Compaq Business Notebook 6720s - Core 2 Duo ...

$700 to $1,118 - 21 stores

HP Compaq Business Notebook 6720s - Core 2 Duo ... $638 to $1,018 - 4 stores

The speed of your computer is determined by the memory capacity, the hdd storage capacity (that means that if the hard drive is full of data your computer becomes low - not about the size of your hard drive) and your processor speed.

In your case I recommend:

1) A good cleaning,
2) Be sure that your computer is not virus or spyware infected
3) Get rid of those programs that you are not using.
4) Disable the programs that are running on the background

Sure after that your computer will become faster.
Your memory capacity is good enough to your normal duties (above described)