There is a process to get software migrated and working on a different system but I sort of do it instinctively and hope I don't leave out any important steps.
You run a monitoring program like
Sysinternals' Process Monitor and take note of the file and registry access, then on the 2nd system you duplicate the registry keys, add the missing files, and in the case of the file you mentioned you need to register it. Process Monitor makes a huge list so you'll need to toggle some of the filters in its settings to reduce that to a manageable level and have as many other unrelated processes and applications shut down as possible to also shorten the list.
To register a file, do that with the Start Button -> Run -> (type) regsvr32 "<path>\NameOfFile.extension", where <path> is the directory where the file is located on your computer and NameOfFile.extension is the name of the file. For example:
regsvr32 "C:\Windows\System32\Mydll.dll"
This portion of my post was copied from this page:
http://consumerdocs.installshield.com/selfservice/viewContent.do?externalId=Q108199&sliceId=1
So after you register it, you may get a new error message trying to run the application, pointing to the next thing you need to do to get it working. You just whittle away till it works, hoping that there isn't some kind of anti-piracy measure that creates a unique hardware ID locking it to the original system it was installed on.
If all this system does is run the dry cleaning software opposed to being a multi-tasking general purpose use system, then it does not need more than 512MB memory to run XP and that one app.
If all else fails, someone may need some hands-on time with the system, perhaps a mom 'n pop computer shop senior employee, someone who actually knows their way around windows opposed to some kid working a Geek Squad desk (or if you are VERY lucky you will find the one Geek Squad employee out of them all that can do it, there's just too much variability in their ablities).
ShYKaGe, I've sent you a personal message.