I just bought an TL-SG105PE but I cannot get it to obtain an IP address and thus I cannot access the configuration interface.

This seems to be due to a faulty implementation of the DHCP protocol.

Upon boot the switch sends a DHCP DISCOVER package and receives a DHCP OFFER from my router. But when the switch then sends the DHCP REQUEST package it uses IP source address 192.168.0.1 instead of 0.0.0.0 as required by RFC 2131. 192.168.0.1 is not on my router's subnet, so the DHCP REQUEST package is blocked.

Please fix the DHCP implementation.

Below is a wireshark trace showing the issue.

Frame 118: 323 bytes on wire (2584 bits), 323 bytes captured (2584 bits)
Ethernet II, Src: 6c:4c:bc:xx:xx:xx (6c:4c:bc:xx:xx:xx), Dst: Broadcast (ff:ff:ff:ff:ff:ff)
Internet Protocol Version 4, Src: 0.0.0.0, Dst: 255.255.255.255
User Datagram Protocol, Src Port: 68, Dst Port: 67
Dynamic Host Configuration Protocol (Discover)
    Message type: Boot Request (1)
    Hardware type: Ethernet (0x01)
    Hardware address length: 6
    Hops: 0
    Transaction ID: 0x000005b3
    Seconds elapsed: 0
    Bootp flags: 0x8000, Broadcast flag (Broadcast)
    Client IP address: 0.0.0.0
    Your (client) IP address: 0.0.0.0
    Next server IP address: 0.0.0.0
    Relay agent IP address: 0.0.0.0
    Client MAC address: 6c:4c:bc:xx:xx:xx (6c:4c:bc:xx:xx:xx)
    Client hardware address padding: 00000000000000000000
    Server host name not given
    Boot file name not given
    Magic cookie: DHCP
    Option: (53) DHCP Message Type (Discover)
    Option: (55) Parameter Request List
    Option: (12) Host Name
    Option: (60) Vendor class identifier
    Option: (61) Client identifier
    Option: (255) End

Frame 196: 342 bytes on wire (2736 bits), 342 bytes captured (2736 bits)
Ethernet II, Src: bc:24:11:xx:xx:xx (bc:24:11:xx:xx:xx), Dst: Broadcast (ff:ff:ff:ff:ff:ff)
Internet Protocol Version 4, Src: 192.168.33.1, Dst: 255.255.255.255
User Datagram Protocol, Src Port: 67, Dst Port: 68
Dynamic Host Configuration Protocol (Offer)
    Message type: Boot Reply (2)
    Hardware type: Ethernet (0x01)
    Hardware address length: 6
    Hops: 0
    Transaction ID: 0x000005b3
    Seconds elapsed: 0
    Bootp flags: 0x8000, Broadcast flag (Broadcast)
    Client IP address: 0.0.0.0
    Your (client) IP address: 192.168.33.194
    Next server IP address: 192.168.33.1
    Relay agent IP address: 0.0.0.0
    Client MAC address: 6c:4c:bc:xx:xx:xx (6c:4c:bc:xx:xx:xx)
    Client hardware address padding: 00000000000000000000
    Server host name not given
    Boot file name not given
    Magic cookie: DHCP
    Option: (53) DHCP Message Type (Offer)
    Option: (54) DHCP Server Identifier (192.168.33.1)
    Option: (51) IP Address Lease Time
    Option: (58) Renewal Time Value
    Option: (59) Rebinding Time Value
    Option: (1) Subnet Mask (255.255.255.0)
    Option: (28) Broadcast Address (192.168.33.255)
    Option: (3) Router
    Option: (255) End
    Padding: 0000000000000000000000000000

Frame 197: 335 bytes on wire (2680 bits), 335 bytes captured (2680 bits)
Ethernet II, Src: 6c:4c:bc:xx:xx:xx (6c:4c:bc:xx:xx:xx), Dst: Broadcast (ff:ff:ff:ff:ff:ff)
Internet Protocol Version 4, Src: 192.168.0.1, Dst: 255.255.255.255
User Datagram Protocol, Src Port: 68, Dst Port: 67
Dynamic Host Configuration Protocol (Request)
    Message type: Boot Request (1)
    Hardware type: Ethernet (0x01)
    Hardware address length: 6
    Hops: 0
    Transaction ID: 0x000005b3
    Seconds elapsed: 3
    Bootp flags: 0x8000, Broadcast flag (Broadcast)
    Client IP address: 0.0.0.0
    Your (client) IP address: 0.0.0.0
    Next server IP address: 0.0.0.0
    Relay agent IP address: 0.0.0.0
    Client MAC address: 6c:4c:bc:xx:xx:xx (6c:4c:bc:xx:xx:xx)
    Client hardware address padding: 00000000000000000000
    Server host name not given
    Boot file name not given
    Magic cookie: DHCP
    Option: (53) DHCP Message Type (Request)
    Option: (54) DHCP Server Identifier (192.168.33.1)
    Option: (50) Requested IP Address (192.168.33.194)
    Option: (55) Parameter Request List
    Option: (12) Host Name
    Option: (60) Vendor class identifier
    Option: (61) Client identifier
    Option: (255) End