First you should have the file scanned here:

http://virusscan.jotti.org/

If it comes up clean, you can try to get some info on it by going to the file and right-clicking on it. Then go to Properties and get whatever info you can (Company, Version, etc.). After that, right-click on it again, and chose Open With...; you may get a warning message, if you do, click on the Open With... button. Choose Notepad (or Wordpad) to open it with. Most likely you will just see a bunch of gibberish characters, but keep looking through it -- sometimes some tell-tale information is provided.

Let us know what you find out

OK, this site (that I'd never heard of) comes up with several of the scanners saying it is a backdoor for a trojan.

File: serimlui.dll
Status: INFECTED/MALWARE
MD5 25e6b8a0bc5fab198ed2ea9619f74074
Packers detected: -
Scanner results
AntiVir Found BDS/Afcore.AH.2
ArcaVir Found Trojan.Afcore.Aw
Avast Found Win32:Afcore
AVG Antivirus Found nothing
BitDefender Found nothing
ClamAV Found Trojan.Afcore-5
Dr.Web Found nothing
F-Prot Antivirus Found nothing
Fortinet Found nothing
Kaspersky Anti-Virus Found Backdoor.Win32.Afcore.aw
NOD32 Found nothing
Norman Virus Control Found nothing
UNA Found Backdoor.Afcore
VBA32 Found Backdoor.Afcore.6 (probable variant)

So I guess this means I should delete it.
I just hope that deleting it doesn't cause my computer problems by not having a .dll that it wants.

Thanks for your help.

Yes, you should go ahead and delete it; I doubt if there is anything in that .dll that your system will want