One thing to do is simplify your system as much as possible before trying any more debugging. For example, among other things, you don't need a hard drive connected to start the debug process and to see if POST can be started. See
As for additional testing the following can
be cheaper than a repair shop test and can be used in the future as well. Only you can judge the economic and time tradeoffs, and whether you want to spend time learning more about your computer. Plus, you may end up spending the money AND then still end up having to take your computer to a repair shop if you can't solve the problem yourself.
You can do a BASIC test of the PSU by using a $12-$15 PSU tester. These testers do NOT test everything about a PSU, but they catch basic/simple problems (like "bad" voltage level). A "Rosewill" PSU tester is on sale with a "promo" code at newgg for $12 at the moment (free shipping).
Or, you can borrow a voltmeter and do some basic tests yourself, looking at the primary DC voltage levels. A cheap voltmeter will cost perhaps $10-$15. Again, this won't show you ALL the things that could be wrong with a PSU, but it's a start.
Depending on what kind of memory you have there are some REALLY cheap memory modules available these days...certainly can be worth spending a bit of money to have the likely "known good" memory to use while debugging a PC. If you go this route, make SURE the memory you get is compatible with your motherboard.
For example, there's a DDR3-1600 1x4GB module currently on sale on Newegg
DDR2 memory is usually a bit more expensive. DDR3-1600 also can be used in a slower computer (e.g. a DDR3-1333 computer, and both DDR3-1600 and DDR3-1333 modules can be used in a DDR3-1066 computer, and so on).
Unable to POST problems are often caused by memory or video problems. Other items (e.g. CPU or PSU problems) can cause similar symptoms but those 2 show up causing POST problems fairly often.