LEDs (Light Emitting Diodes) need a power source to produce light.
Image above is one IR led powered by a 5 volt USB connection.
There are several ways to power your leds. For example by batteries (1,5 volt), USB (5 volt) or a 12 volt adapter. But you could also connect your led's to the 12 volt molex connector on an old pc power supply. Since I'm going to use 100 (mA) miliampère leds, I'm going to need a pretty good power source.
Using batteries doesn't make alot of sense, since you would need quite a few and you would need alot of wire as well, because of the inefficient power circuits.
Using USB is possible, but I would only choose that option, if you are going to use 20/30 (mA) led's and even than, an old pc power supply would make more sense, since you can put more led's in a row.
Why not use an old pc powersupply? Your screen is going to be near a 220 volt power source anyway, since you have to use a beamer and a pc as well.
You could use one of the molex connectors on the computer you are working on, to supply the leds with power. But you could also use it without the motherboard in between.
Image above: 6 IR leds powered by a 12 volt molex connector inside a pc.
Because basically there's a pretty easy solution to hotwire that old pc powersupply.
If you look at the ATX connector, you see several colored wires:
To hotwire your pc powersupply, simply connect the green wire with any black wire (ground) of the pin out and you will be able to connect your leds to one of the molex connectors, without the help of a motherboard, turning the power supply on.