Firstly, you've clearly got the eye for detail in a camera - it's not like you're taking the wrong pictures, but they are 'burning' in the foreground (flash) and the background loses exposure.
There are a few ways to overcome this...
One way is to get a camera you have more control over... But that answer is not reasonable nor one that you need right now.
So this is my suggestion(s)... (keeping it in mind I no longer use a point and shoot so I hope that the ideals of photography follow through).
Light - light is the most important thing to your subject via the CCD in the camera.
eg:
The background in this picture is close enough that it is illuminated by the flash, but at such an angle that the subject does not cast a shadow. That's the important part of the trick to avoid flash burn and lost backgrounds.
Second example:
Now this one is taken using a tripod and a very still (calm) day outside (under shelter). Nothing moves - that's the important part (hence the tripod)... The shutter is set to a timer (this one I can't recall how long, maybe 3 seconds) - dependent on the light. This is where you'll need to trust your camera and it's exposure limiting etc - you'll need to consult the owner manual for the manual settings.
Normally I use a medium F stop (around 8 ) for a macro and then the time is dependent on light. Your camera normally displays the exposure (as a 2 digit decimal number between -5 and + 5 where negative numbers are under exposed and positive are over exposed). Your camera should display those (I hope). Or you'll need a light meter - and to be honest, I doubt that's your best option.
Then finally...
Luck... Without it you just would be in the wrong place everytime
This is taken in full light with no flash and no tripod... The subject is a native bee only 5mm in size. I just waited at a flower that they were visiting until one came along... Luck.... Being in the right place at the right time...
So - in this lesson - if your subject stays still for long enough you can open your shutter and create an awesome photo with ample light and exposure... At the right angle you can get a decent background with almost no flash burn.... And in the right light you only need the right subject to get the shot you want...
So options for you are open...
Get a lamp and shine it on your subject - I find using fluoro better (eg 11W energy efficient bulbs (not to hot) and use in a spot lamp for around $19 at Bunnings). Make sure the light is well behind the camera - the same as the sun should be. When the light goes in front of the camera you get a silhouette:
Like so...
Good luck... let me know if I can help you or even if I have confused you so I can try to clear it up... Good luck... and I want to see some awesome photos... But unlike Kristy, I'm not greedy, I just want good photos - no animals please