Hello Natalie,
Ive had a look at your telly and i have an xbox360 myself so hopefully we can sort ya out. Right here we go,
It appears that your television does not an input called a 'Component in'. you can see this input as it is usually at the back of the television and has 5 sockets that would normally accommadate the cable you found in the box when your hubby got the xbox. This is whats known as Analogue HD.
Now, what you do have is a socket called a VGA ( its usually blue in appearance and very common on LCD monitors. This is also another method used for connecting HD sources. Still with me???!!
If you had purchased the new Xbox360 Elite which is a revised version of the xbox and is available in the states then you could have used and HDMI cable. One single cable that carries the video and audio signal to your HD telly. Tvs are featuring as many as 3 of these inputs.
So my recommendation is that you get a Microsoft VGA HD cable for xbox360 from your retailer. ive provided a link to the official xbox website that will show you what it looks like!!!. Good luck i hope this helps!!
http://www.xbox.com/en-GB/hardware/x/xbox360vg ahdcable/
Of course the xbox will work with the bundles cable but as you mentioned you are left with a few cables thus unable to game in HD!
Regards
Stu