the screen on my monitor has started to irratically change shapes whenever it wants... sometimes the kids will mess w/the buttons on it so maybe they changed the settings? I just dont know how to fix it...

Does it look like its "melting"? like strange shapes, blobs and dark spots or is it more like the type is too large for the screen or too small? Like you cant see all of a page?

you could check if the plug for the monitor is still firmly in the pc and monitor and you could check the vga cart is still stuck in completely on the motherboard , sometimes its the little things that make it go hawire .
some viruses make the monitor do funny things i think others on the board could help you with that
if its a tv type monitor it might just be the monitor bailing out .

Most monitors have a 'reset'/'autoadjust' button or a 'degauss' function - what happens when you use one of those items?

there must be a short or something.... the viewing area becomes distorted in the shape of an hourglass and I have to tilt the screen down. Theres something wrong with the connection in the base, its not the plug.

sound like one of the coils in the back of the monitors has stopped working or doesnt get a signal no more they pull out the beam that gets send out from the base of the monitortube and make lines out of it wish makes the image on the screen
you could try to hook it up to another computer to make sure if its realy the monitor itself .
you say that holding the plug in a certan way to the base makes the monitor work good again .open the monitor up and start with pushing down all the little plugs on the circuitboard and check if this gives an improvement .
if that doesn help resolder the connections of the base to the printboard again , it might have a loose connection on the board inside the monitor its not realy hard to do you do need to unplug it and let the power out by shorting the prongs of the powerplug with a screwdriver to maker sure you dont zap youreself when touching the inside theres some real strong currents going on in there .
and you need a small 10/15 watt or so soldering-iron and thin solder with resin in it to make sure you dont need to put to mush heat intoo the print to get the solder to flow out else you might burn the copper tracks on the board or the plastic inside the plug .

you better try this as a last resort shortly before buying a new one cause theres a big chance it will stop working alltogether

If it's a CRT, I would toss it and get a new one, they're so cheap these days. Here's the kicker though, there are toxic materials in those monitors, so you're supposed to carry it to a place that will recycle it. Most local cities have a place like that (it's no charge to you).