Dell dimension 4300s want to move hard drive to a new machine

To copy and paste you must select the desired text > right click and select copy > move to where you want to paste > right click and select paste.
An alternate method would be to select the text > press Ctrl + C > move where u want to paste > press Ctrl + V

you need to post the Power LED and Diag LED status from the rear of the computer, as they have information on why the system isn't booting.
http://www.fixya.com/support/r4282412-find_no_post_diagnostic_information_dell

Borrow one from a friend and install it by using your key. Later you will have to install all the drivers.

get a windows disk or linux unbuntu , set bios settings to boot cd/dvd drive 1st

Dell chassis cannot accept a Non-Dell Motherboard with out modification. Generally simpler to use a Dell branded motherboard. You can get one here: http://shop.ebay.com/i.html?_nkw=dimension+5150+motherboard+&_cqr=true&_nkwusc=dimension+5150+motherbaord&_rdc=1

your hard drive is full

ive circled the 2 points where you need to push in, the case will open towards you

That particular Dell uses a power supply with non-standard wiring. The plug is the same size as an ATX plug, but it's wired differently. If you were to replace motherboard & plug in the standard power supply, it would damage the supply, or the motherboard, or both. Also, the front panel plugs (for power & power LED & hard drive indicator) are proprietary as well. Ideally you should replace it with another Dell Dimension 4600 motherboard. I've found replacements for reasonable prices on some of the auction places on the web. I recently replaced a failed motherboard in my Dimension 8300 with one I got from a popular auction site, I think my cost was about $59 plus shipping.

The other option would be to remove the hard drive, video card (if any), and optical drives, and consider a 'barebones' package from various sites such as geeks or newegg.

The audio drivers should be here: http://support.euro.dell.com/support/downloads/driverslist.aspx?c=uk&l=en&s=gen&ServiceTag=&SystemID=DIM_PNT_P4_4300S&os=WW1&osl=en&catid=&impid=