We cannot advise on using Action Replay (or any cheat device) on PSP Go firmware 6.37.
Buy games on PlayStation Store (via PC/PS3/PSVita download → transfer to PSP Go via Media Go / QCMA) or play homebrew legally (emulators for owned ROMs, ports like Cave Story, Doom) using Infinity 2.3 on 6.61 (latest OFW) — safer, supported.
Enjoy the PSP's excellent library legally.