Ashley, It worked!!!!!!
Does this still happen on the 64-bit version of C2? The OP error message indicated a 32-bit install of Construct 2.
I've looked in to this, and it appears Windows simply has a hard limit of 10,000 UI objects, even in the latest versions, which sucks. C2 also provides icons in 3 sizes (16x16, 32x32, 64x64) so with 2000 object types in your project you could get up to 6000, and then I guess there's a bunch of other UI stuff going on, so it hits the limit and basically the UI starts falling apart as it can't allocate any more UI objects from the OS.
I've read a few posts by MS engineers along the lines of "10000 should be enough for anybody" (sigh) so doesn't look like this will change any time soon. I will review the code in C2 and make sure it's as efficient as possible, but I'm not sure how to avoid creating all the necessary icons for components like the project bar, where it needs to be able to show everything at once. Icons are also already lazy-loaded per size requested so that should keep the counts down too. Perhaps there's something else I'm missing, but I'm not sure what it could be.
Possible hackish workaround - do not attempt if you're not comfortable with possibly system restoring/booting in to safe mode to fix things: from what I've read you can increase Windows' limits slightly, by modifying the registry. Head to HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Windows. There are two keys initially set to 10000: GDIProcessHandleQuota, and USERProcessHandleQuota. Set them both to 18000 (decimal) and reboot the machine, and hopefully C2 will have more breathing room with icons.