I have a 1080p lg hdtv. I also have an hdbox.I'm getting a 1080i picture. What can be the problem

1080p video resolution can only be achieved by a Blu-ray Disc. Satellite TV, broadcast TV, cable TV do not actually send out 1080p resolution. So unless you are using a Blu-ray movie, you will not be viewing 1080p. Your HDTV has a NATIVE screen resolution and the TV will SCALE all incoming video to its native resolution. Most people cannot tell the difference between 720p and 1080i. 1080p signal sources are slightly sharper. But if you have a HDTV that is 1080p capable and you give it a 1080p source (Blu-ray Disc) and use a HDMI cable to connect, you will get 1080p, you do not have to change the HDTV as it will automatically display 1080p.

If you're using an HDMI cable your display will automatically adjust the settings based upon the video source. Make sure that your source is capable of outputting 1080p. If it's an HD Cable Box or DVR, the maximum resolution it can display is 1080i. If you have one of these HD boxes, set it to only display 1080i as there will be a delay every time you change channels from a channel that is not naturally at 1080i.
If your source is a standard DVD player, it can only display images in 480i (or 480p if it is Progressive Scan) and therefore your TV will display the picture in 480 resolution. If your source is an upconverting DVD player it will display up to 1080p however, Keep in mind that DVD's are in 480 resolution and that regardless of upconversion (or upscaling, though improved, the picture will not be in HD.
The only way to achieve a true 1080p (not dpi... that's dots per inch... that's a printer term. The "p" is for Progressive Scan as opposed to an "i" for Interlaced) is from a 1080p source, i.e., a Blu-Ray disc player playing a Blu-Ray Disc with the use of an HDMI cable. Component Cables can achieve 720p/1080i only with your TV as it does not support 1080p over component cables.
As an aside, there are some media players that support 1080p output and some DirecTV Boxes and DVR's d oas well for 1080p Pay Per View movies.

1080i vs 1080p - Similarities and Differences Between 1080i and 1080p
How 1080i and 1080p Are Both The Same and Different
1080i and 1080p are both High Definition display formats for HDTVs. 1080i and 1080p signals actually contain the same information. Both 1080i and 1080p represent a 1920x1080 pixel resolution (1,920 pixels across the screen by 1,080 pixels down the screen). The difference between 1080i and 1080p is in the way the signal is sent from a source component or displayed on an HDTV screen. In 1080i each frame of video is sent or displayed in alternative fields. The fields in 1080i are composed of 540 rows of pixels or lines of pixels running from the top to the bottom of the screen, with the odd fields displayed first and the even fields displayed second. Together, both fields create a full frame, made up of all 1,080 pixel rows or lines, every 30th of a second.
In 1080p, each frame of video is sent or displayed progressively. This means that both the odd and even fields (all 1,080 pixel rows or pixel lines) that make up the full frame are displayed together. This results in a smoother looking image, with less motion artifacts and jagged edges.
Differences Within 1080p 1080p can also be displayed (Depending on the video processing used) as a 1080p/60 (Most common), 1080p/30, or in 1080p/24 formats. 1080p/60 is essentially the same frame repeated twice every 30th of a second. (Enhanced video frame rate.) 1080p/30 is the same frame displayed once every 30th of a second. (Standard live or recorded video frame rate.) 1080p/24 is the same frame displayed every 24th of a second (Standard motion picture film frame rate.)
For more detalis visit http://hometheater.about.com/od/televisionbasics/qt/1080ivs1080p.htm

1080i or 1080p are both HD. the i and the p stand for the way the images are displayed. 1080i is interlaced, and 1080p is progressive scan. 1080p is the best hands down for fast moving sports and things like that, but for just watching your basic night time lineup, 1080i is fine.

All TV signals, including SKY, are transmitted at 1080i and 50hz. The only sources for 1080p are Blu Ray, XBox or PS3

Most likely it is not a 1080p set. At 32 inches, you will never notice the difference. I just looked up that model number and its 720p native.

HDTV capable: Yes (up to EDTV, 480p)

got to go through your settings and set it to 1080 p if it did not come pre set to that setting..it should have....

Have you made sure the box is set to send a HDTV signal to your LG? Example 720p, 1080i, or 1080p? You usually have to set the resolution in the v+.

I had the same issue. I think you have to reset your PS3. I don't remember how I fixed it but I did find the anwser in the PS3 user manual "Trouble Shooting".