Unfortunately, your Powered Device (PD; the device receiving PoE, in this case your TP-LINK TL-WR743ND AP) doesn't seem to support standard IEEE 802.3af PoE, it supports a nonstandard scheme called "Passive PoE". The nonstandard "Passive PoE" assumes only a 100Mbit/sec connection, so only two twisted pairs of conductors in the cable are used for data, and the other two pairs are used for power. The PD is expected to pull power over the non-data pairs without having to negotiate anything with the Power Sourcing Equipment (PSE, the switch in your case). Thus, it "passively" draws power on the non-data pairs.
It looks like your TP-LINK PoE Switch (TL-SG1008P) acts as a standard IEEE 802.3af PoE PSE, which won't allow much power to be drawn until the PD must actively negotiates how much power it needs.
Shame on TP-LINK for shipping some devices with nonstandard PoE implementations and not being more clear and up-front about the fact that they won't work with standard implementations.
2Only the WAN on the AP supports PoE, and only 4 of the 8 ports on the switch provide it. Are you using the right ports for PoE? If you use the passive PoE power injector that came with the AP, does it power the AP? – Ƭᴇcʜιᴇ007 – 2016-04-02T18:19:53.460