Probably the system board, or maybe this little part called the DC-DC converter. Laptops don't have very many seperate parts, usually everything is on 2-3 large assemblies.
If the system board is gone (which is probably is) it is probably beyond economical repair, unless you just luck out and find someone that just happens to have the part. Usually most system boards for laptops run anywhere between $150-500 depending on the make/model of the laptop.
Shuttle AK31v3.1 AMD XP1700+ 256MB Samsung PC2100 DDR nVidia GeForce2 GTS 32MB
Maxtor 40GB D740X 7200RPM ATA-133 Generic 52x CD-ROM Tekram DC-390U2W SCSI Yamaha CRW8424S CD-RW SCSI-2