Booted up the Xbox after years only to find that the screen alignment is horribly off. Tried adjusting the video settings in Dashboard to no avail. Can't find anywhere that will allow me to configure the alignment or calibrate it.

Was wondering if anyone had any ideas or advice?

In XBMC you can calibrate the screen. I don't know of any other dash that allows it. Are you sure the cables and connections are good. It doesn't make much sense that an Xbox pulled out of the closet and connected would do that straight away.

How are you modded?

If you are talking about overscan alignment (i.e. not all of the text being visible on the screen) then you can alter the display screen size in UnleashX in the same way you can with XBMC - it's under system settings.

For EvolutionX you can achieve the same effect by manually adjusting the position of text on the screen by editing evox.ini or the skin.ini for your skin. For my PAL TV and my 1.4 Xbox the top right and bottom left on the visible screen are at 42,20 and 598,432 respectively, but I have to tweak those settings for each Xbox and each TV individually, because each video encoder and each TV have slightly different amounts of overscan. Just find all the lines in evox.ini or skin.ini (skin.ini takes precedence) that look like:

Text = 28,39,0.5,0x808080,0,"<Time>"

and adjust the first two numbers so that the text appears fully on your screen. Note that for the standard Evox config the text is shadowed, so you have to edit the lines in pairs. For my Xbox I've edited the lines so they look like:

#Text = 30,37,0.5,0x000000,0,"<Time>"
Text = 42,20,0.5,0x808080,0,"<Time>"

FYI, the line format is:
Text = x,y,opacity,colour,alignment, "text or variable to be displayed"

x = horizontal distance from origin in top left (larger numbers are further across the screen)
y = vertical distance from origin in top left (larger numbers are further down the screen)
opacity = how transparent the text is, between 0 and 1.
colour = 0x followed by RGB value pairs (in hex) for the colur of the text. It only seems to use the first digit of each pair for the text colour.
alignment = 1 or 0. 0 means align the left edge of the text with the x and y values, 1 means align the right edge of the text with the x and y values.

If you are talking about more extreme misalignment then it's more likely to be a cable / connection problem as 1hotjob suggested.