There

One missed step in the above -- after renaming l3codecp.acm (which is likely to be l3codeca.acm in current installs) to winemp3.acm, you need to open the Configure window in PlayOnLinux, select the Wine tab, and click the Configure Wine button. Then select the Libraries tab in the box that pops up, click in the New override for library text field, and type "winemp3.acm" without the quotes. Hit enter, then click okay in the warning about changing the loading order. If you miss this step, jukeboxes won't work in world.

Some of the old installation methods don't work the same way in current versions of Linux (Debian Wheezy based distros, for instance) and it's now much easier to install using PlayOnLinux -- if you don't have that package, get it, and install a recent version of Wine into it (Tools menu, Manage Wine Versions, 32-bit tab, then select a recent version that doesn't have a program name associated and click the right arrow button; then wait while it installs), then follow along.

I just installed There, by the following method (this was done on Kubuntu 14.04 and used Wine 1.7.23, but should work in any Debian Wheezy based Linux and with a broad range of Wine versions, and probably in other distros, as long as you have a current version of PlayOnLinux and an Xwindow type desktop, i.e. don't run directly at command line):

Create a new PlayOnLinux virtual drive (Configure, New, select 32-bit, select the version of Wine you just installed above, and give the new virtual drive a name that will let you keep track of what's in it, like There -- strongly recommended to keep each game in a separate "bottle").
Click on the new drive in the list in the Configure window; select "Install components".
Install the following:

d3dx9_36
Flash Player (recommended: check box to allow Adobe to update) (I didn't install Flash Player_ActiveX, and it seems to be working fine; if you have problems with game menus and dialogs, try the ActiveX version)
msxml3
wmp10

Open a terminal and issue the following commands (as regular user)
export WINEPREFIX=/home/Username/.PlayOnLinux/wineprefix/There
export WINEARCH=win32
winetricks ie7 (during install, uncheck "latest updates" and decline -- three times! -- a restart)
Close the terminal; we're done with it.

In PlayOnLinux Configure window, click Wine tab, then Windows Reboot button.

Open a file manager with root privilege (how to do this varies on different systems). Rename winemp3.acm to winemp3.acm.bak. Right click, copy l3codecp.acm, then right click on empty space in the folder and click "paste"; when prompted for another name, enter winemp3.acm.

Back in PlayOnLinux (still in the Configure window): click Miscellaneous tab, then "Run a .exe file in this virtual drive"; in the browse box, find your way to the downloaded "GetThere.exe", select it, and click Open. Wait for the installer to complete. If it crashes, try again; it crashed for me the first time I ran it on both installs today, and went through without a hitch on the second try.

When installer finishes, you'll be back at PlayOnLinux Configure window; click General, then "Make a new shortcut from this virtual drive"; in the box that comes up you should see There.exe, theretweaker.exe, and a number of other items (if those two aren't there, select "browse" and click Next, then click the Browse button, and browse into the virtual drive to find those two items, one at a time); select There.exe and Next, then theretweaker.exe and Next, then "I don't want to make another shortcut" and Next. You'll have three new icons on your desktop (you can delete the one that ends in .lnk; it's a Windows shortcut and Linux doesn't know how to use it).

Last thing is to correct the program call paramters in the There icon; this may differ if you're not running KDE, but shouldn't be completely unfamiliar in other desktops: right click, and select Properties, then Application tab. Click into the Command field and go all the way to the right, remove the %F and replace it with:

-U -l www.prod.there.com/status/min.html

Save the changes to the icon properties, and we're done. There should start normally and run correctly, including with music boxes. And this takes less than twenty minutes to do.

Oh, I forgot to mention: I'm able to use DX9 rendering after installing this way.

If you have an Intel 945 graphics chipset (common in laptops and all-in-one computers from a few years ago), don't bother installing the d3dx9_36; DX9 apparently isn't supported on that chipset and you'll have to use either OGL or DX8 (DX8 works sometimes and sometimes it doesn't in post-resurrection There client, so OGL is recommended, though DX8 worked fine in Windows on this machine). Lack of DX9 support caused the installer to fail on my Dell Latitude D520 at the point it would have let me log in; I went ahead and created the shortcuts and used theretweaker to change the graphics renderer to OGL, and the graphics work fine, but I'm having trouble with Flash (menus and compass) and have no music players (despite the installation of wmp10 and renaming of files as above), though world sounds work fine.

I got Wine to install and run There.com, but when I get to the login screen it's just black. prntscr.com/1xsymc
this is a screenshot of what I get when I close it.

It works in Wine 1.3.31!

Currently it's in very limited public testing before reopening (only 50 beta members at a time, purged roughly every 2 hours) and so far I only managed to get in once with it working properly in Wine and a couple times before that in VirtualBox.
Actually it's not fully working, the browser doesn't work right and I needed to do the email verification at first login through VirtualBox. The problem is that pages intended to be loaded in-game go through the IE file downloader instead of loading in the browser. Apart from the browser, it appears to work perfectly, at least in OGL rendering mode.

I won't post test results until it's officially reopened and I have more time and freedom to test. Right now if I get logged out, I'll probably be waiting a few hours before I can get back in.

Here's the needed launcher script, modify as necessary.

#!/bin/bash
cd "~/.wine/drive_c/Makena/There/ThereClient"
env WINEPREFIX="~/.wine"
wine "C:\Makena\There\ThereClient\There.exe" -U -l www.prod.there.com/status/min.html

Sorry, here's the working script, also removing the unnecessary env line (add it if using a separate prefix). Apparently using ~ for the home directory with quotes doesn't work properly in the cd line, so the client couldn't load any local/cached content.
The direct path in quotes is what I prefer, but you could also use ~ without quotes and any spaces escaped.

#!/bin/bash
cd "/home/[USER]/.wine/drive_c/Makena/There/ThereClient"
wine "C:\Makena\There\ThereClient\There.exe" -U -l www.prod.there.com/status/min.html