AutoCAD LT
OP I go back and forth from AutoCAD Mechanical and Revit Structural at work, to AutoCAD 2011 when I do work at my old boss' office, to AutoCAD LT 2013 and Inventor LT 2013 at home. Between the AutoCADs my biggest tripping point is the use of Mline in full AutoCAD vs Dline in LT. LT might not have everything the full version has, but it's still plenty powerful, and for the 2D production it's aces. I don't know what all your office does with your existing program, but the biggest adjustments will be in going to use of the ribbon. It has been pointed out that you can set your workspace to maintain the "classic" features (so your staff can keep on working with some familiarity), but it would behoove all of you to learn how to use the ribbon a little at a time, and wean yourselves off of the classic workspace. Thankfully, through the CUI you can still customize things to suit your work methods. I found that the way I set mine up works similarly to the old flyouts.
Perhaps the worst aspect of 2013 (and 2012) -- LT and full -- is the new version of array, but there exists a way of bringing back the classic version somewhat.
As for general improvements, back in 2008 autodesk introduced a wealth of improvements for 2D production. It is now possible to create linework, text, dimensions, blocks and hatches that adjust themselves automatically in regards to different viewport scales -- as opposed to having to create separate ones (on separate layers) for each scale. You can also override layer color and linetype on a per-viewport basis, meaning no more bringing an XREF in twice (under two different names) to have one full color and one background gray, for example.
There are tools for adding leaders with keynotes automatically, and adding joglines in dimensions while maintaining their associative properties, and for equally spacing dimension strings. You can create dynamic blocks now (one block has many functions, and/or replaces several blocks). You can now use a Sheet Set Manager. Again, given that your office does mostly 2D production using 2005, I am not sure anyone is using any of these func tions anyway, although I think the SSE at least was available in 2005. Regardless, the potential is there for very noticeably increases in productivity!
A few last ideas would be to a) get your office on a subscription, and b) purchase one copy of full AutoCAD in case 3D projects come up. LT can be used to set up production sets based on 3D content, but can only draw a "pseudo" 3D itself. Oh, and if you start down this road, turn off SAVEFIDELITY! Good luck 
Best thing you can do is download the LT 2013 Trail and see what's what.
You can dowload 50 Trails if you want. All you would need to do is ask each users to create an account individually.
I am using LT 2012 on an XP machine and have been happy with the setup. My belief is that not having Win 7 on the older computer architecture is the key. Not so many bells and whistles clogging up the RAM pipe. This machine also has a dedicated graphics card that makes a world of difference.
All newer version of AutoCAD will open older versions of Drawing files. Your biggest issue would be if there is 3D or third party content that LT does not usually support. But - you may start to use 2013 program content that has trouble going back to 2005 if you keep those. -EXPORTTOAUTOCAD is a function that Dean will advise you to use to solve that issue. Again, download and try.
Any time you use Volkswagen parts on BMW vehicles you are likely to have glitches to work thru.
While using different OS's may not be the most ideal I suspect that most all of your worries and glitches can be solved readily.
Download the Trail (ninth or tenth time someone here has said that?) and give it a go.
Go back thru this thread and write down all you questions and try each one by one.
If your company is having this much heartache over what to do it would seem reasonable to me to task someone with a Win 7 machine loaded with LT 2013 and a XP machine loaded with AutoCAD 2005 to sit side by side for a couple hours a day and try it out. Find out what the issue you have may be.
Just using the same machine that I have had for over 6 years now.
I'm in the process of replacing the machine but as with those who still use R14 it does what I need and ain't broke.
Nvidia GeForce 9500 GT 1 Gig onboard RAM. Over the top for my need but works well.
On the subject of Full: HUGE pricetag up front and if you are doing only 2D drawing then LT is very capable of filling those needs.
Not sure about "10" clicks to place a window. I can choose it, place it, rotate it, size it, and trim it in four clicks I do believe.
