Haha, I thought you gonna go for the 5870? 

Blurriness: What's the native res for your monitor? 720p or 1080p or 1080i?
Not an expert in monitors:
1) but I think you need to use the HDMI cable to hook onto your LCD to your card, see what does this do first,

2)Alternately you should set the 'HDTV support' on the Catalyst Control Center.
Ok, Open CCC > Go to Graphics, choose Desktops & Displays, then right click the bottom small monitor icon and click Configure> HDTV Support
At this point, try adding the desired format, fiddle around until you can remedy this problem.

Not sharp is caused by the resolution problem. In your case, not sure why it don't support 1920 x 1080. What catalyst version of driver u use? I used V10.4, 10.5, 10.6 and now 10.7.
I am also using hd5850 (with VGA cable + DVI Converter) and hook up to 32" at 1920 x 1080, the screen look very sharp. 
Try to play around with the resolution and try again. Update ur driver may help. 

Just 'Right Click' anywhere on your Desktop and select 'Catalyst ™ Control Center' OR it's that red 'ATi' icon in your Tasksbar.
Remember to try both of my troubleshoots ( 1. try use HDMI cable and 2. fiddle with the Catalyst HDTV settings)

Some LCD reso are maxed @1600x1200, but DO PROVIDE details of this LCD monitor of yours, what exact brand, series, etc....probably I can look around about your monitor..

Agreed with JoBigShow. We need the LCD spec and type. I have tried on Toshiba 32" LCD, the resolution supported is so limited. As for my Philips 32" LCD, on default already in nice and sharp resolution.

get the hdmi cable..

To monitor your CPU temp, you need to download: http://www.techpowerup.com/downloads/1691/..._Temp_3.40.html
Once you installed the software, do drag the '.exe' file to : Start > Open Programs > Startup (folder) so you can start monitoring your cpu temp every time you started your PC.

Anyways, back the LCD issue, I've check your LG, and it's a pretty great LCD for it's price.

Now you need to initiated the 1920 X 1080 reso, before buying/getting an HDMI cable:
~do fiddle around with the LCD's Setting if there is an option to change resolution
~usually you change resolution from Windows & Catalyst, so open up Catalyst Control Center or right click on the Desktop an click 'Screen Resolution' to change it via OS.
In Catalyst, go to: Graphics > Desktop Properties to select your reso.

I think you don't need to get HDMI cable considering you haven't change the resolution settings yet, probably by default the reso is 1600 x 1200, so you need to set it to 1920 X 1080.

CPU temps depends on the cooler itself, stock cooler have high LOAD temps and mediocre IDLE temp.
Since you have a quad ( i5) there will be up to 3 proc you need to monitor.

For better cooling, you need to get aftermarket coolers. 

Alright, have you found this on Catalyst yet?
[attachmentid=1698740]

Open CCC > Go to Graphics, choose Desktops & Displays, then right click the bottom small monitor icon and click Configure> HDTV Support

But I think you need the HDMI cable to get this 
Just try anyways to see if there's similar settings for the VGA/DVI... (I forgot since I stop using D-sub VGA & DVI since I got my 5850 end of last year..)

Anyways there's quite a number of settings in Configure for you to fiddle around with, see if you can manage to set it to the right reso...

Haha. how did you do it?!!!
I remembered couple of posts ago you were stuck at a lower res...