They applied in 2000 fair and square when there was barely an "i" anything.
Historical note: there were plenty of "i" names back when the internet was just getting popular. Apple didn't invent the idea... they just used it like everyone else.
That's why Apple's ad agency talked Steve Jobs into using "iMac" instead of the name he wanted to use (the "MacMan"... a horrible takeoff on the Sony Walkman, PacMan, et al).
I recently found a internet/interactive i-trademark and i-name list I compiled a while ago. Here it is. Enjoy!
Red = Apple trademark,
Blue = a name or trademark later used by Apple.
1987 - iNet (online storage)
1992 - iScreen (online computer manuals)
1993 - iTV (interactive TV)
1993 - ICONNECT (internet professionals)
1994 - iPod chair (internet equipped pod chair - Australia)
1994 - iBank (remote banking comms)
1995 - iCOMM (internet comms)
1995 - IMall (internet business)
1995 - iNET (internet comms)
1995 - ishop (internet store software)
1995 - IStore (internet shopping)
1995 - iRock (internet music radio)
1995 - I-SITE (internet comms)
1995 - I-FAX (internet to fax)
1995 - I-Central (internet consulting)
1995 - iFind (MCI directory)
1995 - IVIEW (interactive USAF viewer)
1995 - ICast (internet broadcasts)
1995 - iCity (internet hosting)
1996 - iHome (intelligent/interactive home)
1996 - iMessage (internet mail)
1996 - iRadio (interactive internet radio)
1996 - iBox (internet computer for home)
1996 - IBrowse (internet browser for Amiga)
1996 - i-Remote (internet TV remote control)
1996 - iBooks (interactive books)
1996 - iGames (internet gambling)
1996 - iMonitor (integrated systems monitor)
1996 - iKiosk (internet printer)
1996 - iName (internet addresses)
1996 - iPrint (internet printing)
1996 - iPhoto (internet printing)
1996 - iCall (internet comms)
1996 - iQuest (QWEST internet)
1996 - i-Page (paging handsets from internet)
1996 - iTel (internet media transfer)
1996 - I800 (internet directory)
1996 - I.CHALLENGE (internet gaming)
1997 - IMail (Internet Explorer Mail)
1997 - iWORLD (internet community)
1997 - iPoint (embedded Internet APIs)
1997 - iPump (internet reference design)
1997 - iMeter (internet meter reader)
1997 - I Antiques & I Collectibles
1997 - i-MAGIC (interactive learning)
1997 - iCube (internet kiosk)
1997 - IPostOffice
1997 - iRenaissance (internet software)
1997 - iCommunity (internet BBS)
1997 - iMatch (internet dating)
1997 - INote (internet note taker)
1997 - Iplay (internet games)
1997 - iPhone (internet phone)
1997 - IPAD (Internet Protocol ADapter box)
1997 - IPad (interactive notepad - Cross pens)
1998 - iMagic (interactive ad company)
1998 - iTourist (interactive ads)
1998 - iGovernment (info)
1998 - itravel (internet travel agency)
1998 - INews (internet news)
1998 - IView (interent adapter)
1998 - iAPP (internet job applications)
1998 - iAnnounce (internet announcements)
1998 - iInvite (internet invitations)
1998 - iNote (internet sticky notes)
1998 - iMac by Apple
1998 - imouse (interactive mouse)
1999 - idesk (internet management)
1999 - iform (internet data)
1999 - iTerm (internet web terminal)
1999 - i-Opener (internet web computer)
1999 - IPOD (internet protocol converter)
1999 - iNews24 (internet News site)
1999 - iCatalog (internet catalog)
1999 - iTours (internet tour booking)
1999 - iBook by Apple
1999 - iFrame (internet photo network)
2000 - ICard (internet bank card services)
2000 - iDirect (internet direct satellite link)
2000 - iVacation (internet home rentals)
2000 - iRad (internet radio)
2000 - iPAQ (internet computer)
2000 - iPod (internet kiosk - NJ company)
2001 - iTunes by Apple
2001 - iPod by Apple
AND my favorite preApple i-Trademark of them all...
A product that used ONLY the lowercase letter "i"...