the correct answer is that it depends when your 2004 model year Crossfire was manufactured. if built on or after 10/1/2003, and you were the second owner, the warranty no longer applies to subsequent owners. however, if it was built before 10/1/2003, the powertrain warranty transfers automatically, without any costs or paperwork, to any number of subsequent owners, until the 7 years or 70K miles elapse.

from page 9 of the on-line warranty manual (Chrysler only displays the warranty for 10/1/2003 and later Crossfires on its website). but if yours was built on 9/30/2003 or earlier the manual will specify what i have highlighted above.

F. Transfer of Powertrain Warranty For Vehicles
Built On or After 10/1/2003
You can determine if your vehicle was built on or after
10/1/2003 by looking for the bar coded label on the
driver's door frame or door opening. Locate the "MDH"
entry on the label. The 1st two numbers are the month
and the 2nd two numbers are the day. The "DATE OF
MFR" entry shows month and year the vehicle was
built.
To transfer the Powertrain Warranty, you must have
an authorized Chrysler, Dodge or Jeep dealer process a
"Transfer of Coverage Application" for you. The cost
for this service is $150. You pay this fee directly to the
dealer. You must apply for a coverage transfer within 30
days from the date you buy the vehicle.

G. No Coverage to Second Purchaser if
Transfer Fee is Not Paid
If you do not transfer the remainder of the 7 year/
70,000 mile Powertrain Limited Warranty coverage
and pay the transfer fee, or if you are the third (or
subsequent) owner of the vehicle, the Powertrain
Limited Warranty described in this Section 2.2 does
not apply to you.